If you had a normal period in July, it is unlikely you were pregnant by the ex then. Also, having sex two days before your period you are unlikely to get pregnant, the egg is not viable. You would be just about at the lowest point of your fertility.
Having sex after your period, on about day 6 of your cycle, it is possible for you to get pregnant. It really depends upon when EXACTLY you ovulated.
A March 31st birthday is 37 weeks after July 16. NOTE: doctors base dates on when your LMP was. Why? Because most women remember that.
It looks like the "new guy" is the father.