Hallow Dear,
I have gone through your complete history. Let me answer your questions one by one:
1. If she had her menses on July 13 and if you had a solitary intercourse on July 14, it is most unlikely that this intercourse has caused the
pregnancy. The egg release takes place 14 days before the next expected menses. Considering her menstrual cycle to be of 30 days, the next menses were expected on August 12 and hence the day of egg release (ovulation) would be July 29. With Last menstrual period (LMP) on July 13, 2010, her due date would be April 20, 2011. Her
ultrasonography calculates it to be April 24 2011, which congruent with this calculation. A couple of days difference is no difference in this calculations.
2. It is possible to diagnose pregnancy even a few days before missing a period by
Beta hCG test on blood.
3. Clinically, we calculate the due date of delivery by formula DD = LMP + 9 months + 7 days. By ultrasonography, the due date is calculated by the size of the embryo, hence it is more accurate. Still usually there is no much difference in these two days. Considering the due date calculated by ultrasonography, she is giving correct information about her LMP as July 13, 2011.
4. Even after considering her history as fool proof, since you had sexual relations with her on the next day of her LMP, you cannot be the father of the child in her womb. However, to prove it scientifically, you may go for DNA test.
I am sure this clears your dilemma.
Dr. Nishikant Shrotri