can taking the pill seriously affect my period?

So I started taking the pill a few days ago. I had talked to my doctor and she told me I could wait until after my period finished to start. If I decided to start right away my period may end up being a little wonky this month. It was supposed to come two days ago but has yet to. So I don't know if by wonky she meant late or that I may just skip a period this month. Any thoughts?