I guess it is from your ex
The way you wrote out the dates above, where you said
"and then 2 days later I bleed heavy and it stopped around may 5 then on the 7th I had sex with my new boyfriend he ejaculated in me then on may 9th I had sex with me ex again he pulled out and after that I had sec may 10 11 12 13 14 15 with my boyfriend after that nobody else I had a false pregnancy on may 18 and a positive one June 5 I went back June 14 they say they didn't indicate a heart beat but I was 6 weeks pregnant not I was going to have a miss carriage on June 21 I had a ultrasound they heard a heart beat they told me I was 6 weeks 1 day and the baby was fine"
makes me think that the part about "June 14 they say they didn't indicate a heart beat" means you were not at 6 weeks by June 14, since they would have heard a heart beat by then (assuming this was done by ultrasound) if you were really 6 weeks along. You say they gave you a weeks count that conflicted with the fact that there was no heartbeat and then wrote off the inconsistency by saying you were probably going to miscarry, but if so you would have miscarried, and you didn't, you have a normal pregnancy. This indicates their explanation of the discrepancy was wrong, not that their weeks count was right.
Your due date from ultrasound evidence is February 13, which indicates conception May 23, and your ultrasound where they heard a heart beat on June 21 and said you were 6w1d computes back to conception on May 24.
If there had been a heartbeat on June 14, you would need to take into account that 6 weeks figure, but there wasn't. It just doesn't sound like you were really that far along at that time.
By all means get a DNA test with both guys when the baby is born, so you can put your worries to rest forever. But in your shoes, during the pregnancy I would assume the May 9 sex was too early to have produced the baby.
Misslovemost, it sounds like you conceived around May 23.
My lmp was February 22. I was intimate two days after my period ended on the 27th. He pulled out which I don't think resulted in my pregnancy (I could be wrong) and we were intimate again on March 6th. I missed my period which was due March 20/21. My first sonogram, at 11 weeks 2 days, gave me an edd of November 28. All of my other ultrasounds go hand in hand with the same due date. When do you think I conceived? I took a clear blue HPT on the 21st of March with the weeks estimator saying 1-2 weeks. Do you think I ovulated somewhere between the 6-8?
If the last time you had sex with your ex was May 9, and if your ex is the person you are trying to rule out, I don't see this pregnancy as coming from your ex.
From your early ultrasound it seems that you conceived at the end of May. Did you have sex with your boyfriend throughout the month? May 9 seems too early.
Did you get the February 13 due date early in the pregnancy from a doctor reading your ultrasound results?