Hi thanks for your question.
The bleeding after intercourse
could be due minor trauma during sex and second bleeding 2 days before could be implantation
bleeding that is bleeding which occur due to the implantation of fertalized ovum into uterus
test usually comes positive 10 days after missed period,may be you have got your pregnancy test done little earlier.Repeat the pregnancy test if still turns out to be negative means you are not pregnant and there may some other reasons for your bleeding.The other way is to go for ultrasound
to confirm or rule out pregnancy.This will also help in determing cause of bleeding in case pregnancy is ruled out.Consultation with gynaecologist is advisible.
Hope this answers your question.