Period&Babies

So, this is just a random thing. But I didn't start my period until maybe 14 or 15 years old. From then on it was never a regular thing. I would go months without having one. Sometimes over six months. I had went to the doctor and they gave me birth control to regulate my period. Which worked of course. A few months ago (I'm 21 now) I had to get my birth control changed because I was having migraines. This kind hasn't made me have a period at all. So, long story short, I've always heard girls who start their period late, or having trouble having one at all, have infertility problems. So I guess I'm just wondering if this is true? Has anyone had this problem? I've always worried about this. I've asked my doctor before about it and she just told me we would talk about it and cross that bridge when we ever got to that point. Sorry about the long post.