Can hospital test me for diabetes?

I don’t have insurance at the moment, I’m 21. For awhile now there are times between meals when I feel so dizzy and faint that I fear I’ll fall over, once I eat something, usually sweet, I feel better almost instantly. I woke up this morning and I have that insanely dizzy, body tingling, faint feeling and I am debating going to the hospital as I’m worried this could be related to something like diabetes. Can they test me for this at a hospital?