You continue to ask anxiety-driven questions about no risk encounters.  While this event is unrelated, it continues your pattern of forum abuse.  You will get a single answer here and the thread will be closed.

This was an essentially no risk encounter.  Syphilis is transmitted through direct contact with an infectious lesion.  Thus touching a lesion could theoretically lead to syphilis but is most unlikely as syphilis is a rare disease and you would have likely detected a lesion if present.   Despite the theoretical risk, in reality the risk of the event you describe is close to zero and there is no medical need for testing.  If you choose to test, a 4 week test would detect most but not all syphilis.  Definitive testing would require tests to be performed at 6-8 weeks.  that you have skin peeling over your fingernail does not change my opinion or advice.  EWH