I have a piece of bark under my nail and can't get it out. I have no insurance or money to go to a doctor. What should I do?

Bark under nail. If it does not become infected (which will present with increasing pain instead of decreasing pain with time), you can just wait. Foreign bodies under the nail, like splinters, will tend to grow out with the nail. If it remains very uncomfortable, you may have an infection that needs to be treated; if it is infected the doctor will remove the bark. But if you can stand it, you can wait.
Be seen. This is a difficult one to answer. I can empathize with your situation but you could be at risk for developing tetanus or some other infection. If there is a free medical clinic in your area i would seriously consider paying them a visit.