Conception date?

I'm very confused about my conception date.  I'm currently 23 weeks pregnant.  On Friday, April 3rd,  I went to the doctor with bad back aches and they gave me meds for a bladder infection, by Monday it wasnt better so the doc called in a different prescription.  I was using the ortho evra birth control patch, and had been for about 4 years.  Well my period was due April 24th and never came, so I took a test and it was positive.  I made an OB appointment for the first of May, and they did an ultrasound and asked what the first day of my last period was (march 20). Then the doc said i most likely conceived on April 3rd.  Well i know I didnt because I was sick.  My husband and I didnt have intercourse for about a week until i was healthy again.  So I know for a fact I couldnt have conceived from April 3rd-12th.  But all my ultrasounds date me right at conceiving around that time.  Is there any way I could have had sex on April 1, or 2, then took the meds on the 3rd, and it cancelled out my birth control and the sperm was still in me from the previous day, and thats how i conceived?  Since I was wearing my birth control patch, the only thing we could think of was that the antibiotics from the doctor cancelled out my BC.  Any suggestions would be greatly appreciated!  

Sincerely,
Confused!! lol