Hi Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern...
No birth control pill should not cause
bleeding after intercourse. Bleeding after intercourse should be due to bleeding from
cervix (the lower part of uterus). Cervix has high blood supply & Even when cervix is healthy, vigorous sex can cause some bleeding. This mostly occurs when you have
vaginal dryness or less
vaginal lubrication. You should use lubricants before having sex.
However bleeding from cervix can be because of some abnormality in cervix. In case of cervix abnormality, even gentle sex in presence of enough vaginal lubrication could cause bleeding. Therefore bleeding after intercouse could be a sign of cervix abnormality.
As you have bleeded twice, so there are chances of some cervix problem such therefore You are advised a
pap smear to rule-out a cervix problem.
Refer to a gynaecologist.
Hope this information helps