Is there a reason you think you might be further along? I'd go with conceiving on September 2nd, but it's not impossible that you conceived on August 10th.
The due date of May 24th, lines up with having a period on August 22nd, and conceiving on September 2nd.
This is always a hard thing to tell. I'd guess the sept. 2 date but your ultrasounds should help with this determination. We have a DNA forum if you are having a struggle for who the father is--- but otherwise, I would think your ultrasound can give you a reading of where your baby is at. I was 10 days late with my first and thought I Knew when I conceived (we were trying) and my doctor said we guess at that-- but she might have been trying to get me out of the office as I wanted to be induced and she didn't want to for first pregnancy. ha. Anyway, good luck hon