Because of this, it may not be possible for us to tell you exactly what is wrong with your hamster. Especially since many symptoms are just signs of pain or discomfort, which can be caused by tons of different ailments. In some cases, testing is required to get an accurate diagnoses.
Vet Care and Hamsters
I'd like to start off this article with one simple statement that I hope will carry through.
Vet care is a requirement for responsible hamster ownership.
There's an unspoken idea that vet care is somehow "optional" or an "extra" for hamster ownership. But the truth is, vet care is just as important as a large cage, safe bedding, high-quality food, and so on.
We place so much emphasis on getting proper food and supplies...but vet care is usually an afterthought (or not even mentioned at all). And really, it doesn't make any sense. Not taking a sick hamster to the vet has a lot worse consequences than having it in a too-small cage or not giving it enough bedding.
I would argue that being able to get your hamster to a vet is more important than providing it with proper supplies.
Put another way...a hamster in a too-small cage will likely be bored and restless. But a hamster with an untreated broken leg will be in horrific pain for a very long time and will likely suffer permanent disfigurement due to improper healing.
Which situation is worse for the hamster?
Common Criticisms of Vet Care for Hamsters (with Rebuttals)
"You can't take a hamster to the vet - vets only treat cats and dogs, not hamsters."
This is simply untrue. Yes, many vets are "companion animal" vets - that is, they work exclusively with common companion animals (cats and dogs). However, those are not the only types of vets that exist. Exotic veterinarians specialize in other small animals kept as pets, including (but not limited to) birds, rabbits, reptiles, amphibians, and rodents. There are vets that will see and treat hamsters. Some even do surgery on them! In fact, there are even entire animal hospitals dedicated solely to exotic pets. So yes, you can absolutely take a hamster to the vet - you just need to find the right vet!

"Vets can't do anything for hamsters because they're so small."
Why would the practice of exotic veterinary medicine even exist if nothing could be done for hamsters?

Hamsters can be given medications like antibiotics and pain medicine. Hamsters can have x-rays and ultrasounds. Hamsters can have any number of tests done (fecal tests, blood tests, etc.). Hamsters can be treated for chronic illnesses like diabetes. Hamsters can even have surgeries.
"Hamsters don't need to go to the vet."
Hamsters are not robots or toys. They are living, breathing animals. They can and do get sick and injured just like you do. They suffer pain just like you do. And if they do, they need medical attention...just like you do. If a hamster breaks its leg or develops a tumor or gets a respiratory infection...yes, it needs to go to the vet, plain and simple.
"It's not worth it to pay vet bills for a $10 animal."
Vet bills ALWAYS cost more than the animal itself, and usually significantly more. This is just a simple fact of pet ownership. It's true for cats and dogs as well - the lifetime cost of routine veterinary care for a dog (vaccinations, teeth cleaning, etc.) is going to be well over the initial cost of that dog.
Consider the following scenarios:
Is a dog that was purchased for $1000 from a pet store more "worthy" of vet care than one who was adopted from a shelter for $100?
Let's say your friend buys a cat from a breeder for $500. They have allergies, and give the cat to you for free. Did the cat "deserve" vet care with your friend (because they paid money for it) but now suddenly isn't "worth it" because it was given away for free?
Vet bills are part of having a pet. If someone is unwilling or unable to pay vet bills, that person should not get any new pets.
"Hamster vet bills are unreasonably expensive."
If you can afford to get a hamster and good-quality supplies, hamster vet bills should be within budget. Yes, vet bills will be the most expensive part of ownership. But hamster vet bills generally do not run thousands of dollars the way dog and cat bills might. It might cost a total of $200 - $300 to get an illness treated - that's including the exam fee, medicines, tests, and follow-up appointments. If it's something simple that requires only one visit and some meds, it could end up being only about $100. It's not absurdly expensive and it's not out of reach.
When it comes to the cost argument, one issue that often rears its ugly head is surgery. Surgery on such a tiny animal can be very, very expensive. I've personally been quoted nearly $1000 for a surgery on a hamster. This is, undeniably, unattainable for some people.
But that's not what this article is about. There's a difference between not being able to afford a $1000 surgery and not even going for a simple checkup and maybe some medicine.
Providing proper vet care does not mean paying for every possible procedure no matter how expensive. It means at least getting the hamster to the vet when needed and being able to pay for basic medicines and simple treatments.
"My hamster is extremely sick / dying. It's going to die and there's nothing that can be done about it, so why should I waste my money going to the vet?"
It's not always about fixing the issue or curing the disease. It can be about something as simple as providing painkillers to ease the hamster's suffering. It can even be about euthanasia.
Taking a sick or injured hamster to the vet should not be about keeping the hamster around for the owner's benefit. It should be about what is best for the hamster.
Follow-Up Questions and Concerns
"I own a hamster (or hamsters) and I can't get to the vet. What do I do now?"
First thing is first. Take a deep breath.
You are not a bad owner. You are not a terrible person. You are doing the best you can.

I'm not going to lie and say that it's "okay," because it isn't. It's not a good situation for you and not a good situation for your hamster.
The first thing you should do is try to remedy the situation. Why is it that you can't go to the vet?
You can't afford it? Start saving money. If you are a minor, talk to your parents. Talk to them about how you want to be 100% prepared to take care of your hamster that you took responsibility for. Tell them how you want to live up to your commitment, but you need some help or advice on how to save money or make a plan. Don't demand, don't whine. But talk.

There are no exotic vets in your area? Start researching.

Do some more searches. Find out if any local non-exotic vets would be willing to at least look at a hamster in an emergency.
Your parents won't let you? Again, talk about how you want to honor your commitment to an animal you took responsibility for. Don't make it about demands, but about needing help developing a plan. Be humble and own the situation.
"What if I still can't get to the vet no matter what?"
If you've tried the above and more and things just are not working out for you, there's not too many options.
If you are really worried and concerned, you may consider rehoming your hamster. This is NOT always the best option, but it is a possibility that could work in some situations.
What really matters is what you do in the future.
If you cannot get to the vet, the only responsible decision is to refrain from getting any more hamsters (or pets) until the situation changes.
It's one thing to get a hamster not realizing the importance of vet care. Again, it's not a good situation, but it's something that unfortunately does happen.

But it's another thing to get a hamster knowing full well that you cannot provide necessary vet care for it. At that point, it is selfish and irresponsible. Because it is putting your want of a hamster over the hamster's need for proper medical care. If you truly care about hamsters, you won't bring one into a situation where it may suffer unnecessarily.
Final Thoughts
1) Responsible hamster ownership requires vet care.
2) We can talk all we want about big cages and healthy food. But not providing vet care has a lot worse consequences than using improper supplies.
3) You want a hamster. A hamster needs a vet. The hamster's needs come before your wants.
4) Making a mistake is not irresponsible or selfish. Continuing to make the same "mistake" over and over again is.
5) Everyone can be responsible and do their part! Sometimes that means holding off from getting a new hamster until you can provide for all of that hamster's needs.