I gave my husband oral sex and a little more than 24 hrs later I have a cold sore outbreak when I didnt yesterday is it possible I gave genital herpes?

Possible. It is possible to get HSV 1 or 2 there but likely are ok as no breakout at time.What is done is done so do not worry about it.Watch for any breakout and treat.you could try post exposure valtrex or Famvir but not sure if would help.