You had your last period on 13 January.
You had sexual intercourse on 06 February.
If your last period was on 13 January then your date of ovulation is about 27-28 January. By 06 February the ovum will be already dead and there is no question of pregnancy. So implantation bleeding is out of the question of .
It is not clear whether you are married or not and how frequently you have sexual intercourse. If you have had sexual intercourse on 06 February but not earlier or later than that date in that cycle then we know that you can't be
pregnant due to sexual intercourse on 06 February. But if you have intercourse frequently then all this calculation is futile.
For more information you may consult with me on Practo.