question about the contraceptive pill ...?!

I used to take the combined pill and was fine with it but basically I was started taking it again for 2 days (started thursday, first day of period) until I had some side effects, it was giving me really bad headaches and I was being sick so I stopped.
so I had 4 days with no pill, went to the doctors yesterday and she prescribed me with a different type of pill with lower oestrogen I think, and I started taking it yesterday like she said even though I was near the end of my period, but I had unprotected sex earlier, not being told that the pill wouldn't start working straight away?? so I should get the morning after pill tomorrow right?