Welcome to the MedHelp forum!
If you have already conceived by Day 15, then your periods will not come. Yes, if you have a mature egg, you can conceive. A progesterone preparation in last half of cycle is given to regularize the cycle and increase chances of pregnancy. If you have doubts and concerns then please consult your gynecologist. If you have trouble conceiving, then you may need more tests. If you have irregular cycle, then also other causes like PCOD need to be ruled out. Take care!