From what I understand, antibiotics CAN make your periods irregular, as can illness (especially one that hangs around for 3 weeks!). It could be as simple as that.......however, I for one was one of those rare people who took multiple pregnancy tests (I believe five or six total - two of which were done at clinics) which all continued to come back negative until I was well over a month late on my period. I can't say now how I knew, but I KNEW that I was pregnant, despite the tests. I even had one nurse try to convince me to make an appointment for a D & C in order to 'jump start my period' again, as my periods have always been like clockwork. I began to worry about other possibilities such as uterine cysts and even more dire ailments, but as it turns out, I knew my body better than the tests did, because I finally did get that positive test I'd been waiting for!
As a side note, I got another surprise during this pregnancy: After having my initial ultrasound and going through all of the monthly OB appointments with normal results - normal fetal growth, normal size for my due date, strong heartbeat, etc. - I finally went in at 22 weeks to determine the sex of my baby. I got some 'looks' upon arriving due to my unexpected (and extreme) weight gain during the past month, but I had no reason to believe that anything was wrong...and I was right...again. Nothing was WRONG! I was having a healthy baby boy........and his BROTHER! Somehow (and I understand this happens more than one would think) the fact that I was carrying twins was unknown to all until that day!
Moral of this (long) story: Anything is possible, even if it seems unlikely! You could be pregnant......I was, even though all signs said 'no'. That being said, remember that a period delayed by antibiotics/illness (or even stress) is quite common and normal, too.
Best of luck to you!