It's difficult to be able to advise you without a diagnosis. There are only a limited number of things that you can do that may or may not help relieve any pain that you are having.
What you describe doesn't sound like carpal tunnel syndrome. With carpal tunnel syndrome the symptoms begin in the fingers and hand and progress upwards to the wrist and into the arm above the wrist.
You are describing what sounds more like a bulging disc in your cervical spine, i.e. your neck that is compressing nerves and spreading down to your arms.
Do you have a burning, stinging and or numbness pain in your arms? That is another good indication of nerve compression as well.
Without seeing a spine specialist and having an MRI done it will be difficult to diagnose you and without any insurance, it will be even more difficult to obtain any relief or get a diagnosis.
You said you went to your school's health center. What kind of school is this that has a health center? Is there anyone that they could refer you to see that would be part of the health center?
Are you in HS or college? Could you still be under your parent's health insurance coverage if you are in school?
Several small thing that you can try that might give you some relief are over the counter anti-inflammatory meds. Ibuprofen is the one that most spine specialists will tell you to take.
If you don't have any health issues that would prevent you from taking it, you could take 400mg every 6 hours or so and see if it provides you with any relief. Tylenol may help with pain for a bit and it may not, but it will do nothing for the inflammation that is going on.
For some reason I have not met any spine specialists that advise taking Aleve, I don't know why, but it is always Ibuprofen.
You can try ice on your neck for about 15-20 minutes then move it down to 1 arm and then the other and see if that helps to relieve some of the pain and shrink any inflammation.
If that doesn't help you could try most heat on your neck for about 10 minutes and then move it to one arm and then the other.
One simple way to get moist heat is to make and use what is called a "rice sock".
Just take a long white cotton tube sock. Fill it about half way or a little more with the cheapest white rice that you can get. DO NOT USE INSTANT OR MINUTE RICE.
Once you have the rice in the sock, tie the open end with a knot very close to the open end.
Then put it in the microwave and heat on high for about 90 seconds. Take it out and spread the rice out smooth to fill the sock and lie flat. wrap in a hand towel and put on your neck, then one arm and then the other.
Be careful not to leave the sock on too long as you don't want to burn yourself.
If thing get really bad with the pain, there is always the option of going to the ER. They can not refuse to treat you even if you have no insurance and most hospitals will have some kind of arrangements that can be made for bill paying and forgiving part of the bill that you owe.
I know how hard it is to be without health insurance and hopefully things will change for you and those that have no insurance.
Good luck and keep us posted on how you are doing.
Fran