If someone suspects they need non-emergency medical care but they have little money, what can they do?

Free clinic or CHC: If you live near a larger city or university town, they may have a free clinic. There are also federally-funded community health centers which see low-income and uninsured patients at a discounted rate. Some docs in private practice may be willing to see you at a discount - ask around. Try calling your local county health department to find out what resources exist in your community.

Sliding scale: Difficult situation. In general an urgent care center would be the choice for non-emergent conditions. Try calling the center and see if they do "sliding scale payments." Depending upon how much you have / money you make there would be a reduced fee. Good luck in your search.