I had unprotected sex on the second day of my period which was April 30th. Then my period ended on the 3rd of may. I had sex on the 16th of may and after 2 weeks was feeling off, and I didn't get my period on the 29th like I should have. So I took a test and got positive. How do I find out what day I really conceived the baby?

There is really no way of knowing which day you conceived.

If I were to guess, and guessin is all we can do, I would say you conceived the second time. On May 16.

If this is a question of paterinty, you will have to wait until the baby is born to have a DNA test done.