Should i be concerned if i had unprotected sex at the beginning of a new birth control pack, but around the same time had 3 to 4 days of diarrhea?

Yes: You should be concerned for stds if you are having unprotected intercourse. You cannot prevent disease with birth control pills.

Use condoms: Unless you know your partner's full sexual history and you know that none of his previous partners had hpv or an abnormal pap smear, you should be using a condom to protect yourself. If you were just starting birth control, you should be using condoms for the first month. If you were going from one pack to the next, you should not be at risk of pregnancy, but could be at risk for diseases.