It isn't really possible to determine what day you conceived when you had sex that often around the actual conception day. The nurse probably just added 14 days to the first day of your LMP, which you say was Sept 15, because you are most fertile mid month. The odds of getting pregnant the second day of your period are low, but there is no such thing as 'never get pregnant' any day of the month.
Later ultrasounds might predict a little bit better, but NO ONE EVER can predict which of your sex partners is the father. You will have to get DNA testing done when the child is born. Maybe with the guy from the 15th, to rule him out, and not even mention it to your boyfriend.
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