Am I able to know the exact date that I conceived if I know the exact dates that I had sex?

If you only had sex once during that 2 or 3 week period, if you had sex several times over a 2 or 3 week period then no, as long as it was the same person no real issue, if they were different men, you will have to do DNA test when child is born

Having sex on a certain date does not mean you conceived on that date as sperm can live a few days waiting for ovulation. For example, you may have actually conceived later that same day, or you may not have conceived until 4 days later.

As Fr_Chuck said, you will have a window of time for when actual conception took place.