From the ultrasound information I don't think there is any way to know. You would have had viable sperm in your body from both guys at the time you ovulated. (According to your doctor, you ovulated on May 23. I am not sure what you mean when you say "May 21st the ovulation started;" ovulation is a one-time event, it happens in an instant and is not a several-day thing.) Living sperm in your reproductive tract from two men means that one sperm made it to the egg and who knows which guy's.
All you can do if you must know before the baby is born is spend the big bucks and get a prenatal DNA test from Ravgen or the DDC. (Don't go with one of the Internet cheapies, they are not reliable.) If you can't afford a prenatal test, the post-natal tests are much cheaper. But in your situation, since you have had an early ultrasound pointing to the time when you would have had viable sperm in your body from both men, all you can do is test. In a really fair world, both guys and you could split the cost of prenatal testing. But if that wouldn't work or you are trying to keep the situation a secret from one of them, I think you need to at least tell the guy you have told is the father, that you now realize he might not be. He doesn't deserve to think all through your pregnancy that he's going to be a dad and then to find out later that a test is needed and he might not be.
How did you get the 5 weeks 1 day count on June 16? Was it from an ultrasound?