I had my first day of period on 9th January. As my menstrual cycle is 23-24 days, the due date of my periods was 2nd February. But it did not happen on 2nd. I had unprotected sex on 4th February, and I took an I-pill for that on same date. I still did not have my periods. Is it because of I-pill or Am I pregnant?

Yes, it is either the I pill or you are pregnant,

A side effect of the I pill can be a missed period. (sometimes but not everytime) The I pill is also not 100 percent effective.

So you will have to wait.

When you are 14 days late do a pregnancy test, and if negative, do one every week, to be sure.

If you still miss period on month two, check with your doctor