Birth control pills may not be the best choice for you. Ask your doc about another option. I've heard of birth control methods that prevent you from getting your period every month. Instead it's something like every few months or a year? I don't remember exactly but it's worth looking into!
Hormonal treatments can wreak havoc on the menstrual cycle. The spotting you are now experiencing may just be a result of the hormones. As for how you can stop it, I don't know what to tell you. If it continues, or gets heavier, it may just be your period. If you are still concerned, going to a doctor would not be such a bad idea.