How did your doctor get the due date of April 28, was it from an ultrasound? If so, how early in your pregnancy was that?
You say "Ovulation day was 8/8, doctors conception date 8/5," but both things can't be true. Where did you get the "ovulation day," from an app?
If I'm understanding the timeline, things went like this:
July 22 -- first day of period
August 3 -- sex (unprotected, without ejaculati0n in your body but with penetration again after ejaculation)
August 5 -- sex (unprotected, with ejaculating in your body)
August 5 -- doctor's estimate of conception day
August 8 -- sex (with pulling out)
August 8 -- estimate of ovulation day from other source
August 11 -- sex (with pulling out)
August 14 -- pregnancy symptom (breast soreness)
Two things about this timeline make it hard to suggest which guy has the stronger chance of being the dad. One is that the guys were very close together in time. Sperm from the first guy on the 3rd (from his first ejaculation, which is not "pre-cum") would have still been alive in your system when you had sex with the second guy on the 5th. (Sperm can live in your system 4-6 days.) The other problem is not knowing the answers to the above questions. If your doctor gave you the due date based on an early ultrasound, you can toss out whatever source told you that you ovulated on the 8th. Calculating from one's last period is inaccurate compared to using an early ultrasound to measure the date of conception.
Just for your future information, having more sex after ejaculation works about as well as if he finished inside you, whether he wiped off and pulled out or not. After an ejaculation, your guy had masses of sperm inside his urethra (out of range of washing the exterior of his penis, and a lot of them out of range even of him peeing). There are millions of sperm in one ejaculation; thousands at least would have been waiting to take a ride in the pre-ejaculatory fluid for the next erection into your body. It's not "pre cum" that gets you pregnant, that fluid (from the Cowper's gland) is sterile. It's the passengers on the pre-ejaculatory fluid bus. And there can be a lot of those, when a guy has just ejaculated.
My suggestion is that you either do a prenatal DNA test, seeing if both guys will help you share the cost (it's expensive) or wait until the baby is born and do a DNA test with both guys then. (DNA testing after the baby comes is about ten times cheaper than doing it before the baby is born.) If one of the guys balks at doing a test after the baby is born, you can get him to do so by court order.
I kind of doubt the August 8 date for ovulation if the date the doctor gave you was the 5th, unless the ultrasound was really late in your pregnancy, at which point it could be inaccurate for the purpose of identifying a conception date. But even if you knew for sure what day you ovulated, it still leaves the identity of the father something of an open question because you had sex with both within three days, and the first sex (though you wrote it off because of the pulling out) did have plenty of opportunity to put sperm in your body due to you going back for a second round.