Take ipill or wait for next period.

My (female) partner & I, involved physically . I ejaculated first time (outside only not in vagina) but i forgot to wash my penis afterwards. So after 2 hours we again tried to be physical unprotected this time but my penis was only very little inside her vagina (as it hurts her very much) but i didn't ejaculated that time and pulled out. My penis was dry that time (previous ejaculated semen was dried out but was on my penis head only) So is it possible that sperms were alive on the top of my penis after 2 hours (head was totally dried out) & entered her vagina which could lead to pregnancy . Also this happened after like 13 days later on 28th when her prev periods started on 15th (ended on 20th). only 30 hrs has passed ,So my question is should she take any birth control pill or wait for her next period which is likely to occur on 6 or 7th. ? Also she has increased testosterone (male hormone) inside her body, so taking ipill will increase her hormone problem or any other side effect?