At the nail salon sunday, the woman cut my skin with a metal nail drill and i started bleeding. i am scared. am i at risk to catch hepatitis this way?

Nobody has ever been known to catch HIV from an injury during any cosmetic procedure. Almost certainly there is no risk. For additional reassurance, contact the nail salon and ask them to confirm that they either do not reuse instruments or adequately clean them between customers. Even if not, there probably is no risk for any blood borne infection. Good luck.