13 years old is too young to be talking about birth control pills.
I don't believe in lying to your child for any reason. They must be taught morals and values. How you can teach them that if you lie to them?
I think your daughter will be just fine down the road. It would probably be a good idea for her to get regular check ups while she's on the pill. I do hope they're helping to get her regulated.
I would've lied and made my daughter think she just on a pill to help with her periods, not necessarily a birth control pill.
It shouldn't. The thing that would worry me more is that she may eventually get the idea that sex is okay because she is on birth control. Make sure she is well educated on the do's and don'ts of this. Blessings - Blu