Always use condoms for backup when put on antibiotics. It's such a simple solution and yet no one ever thinks of it. Not sure why that is.
I would ask the pharmacist. Interaction between antibiotics and birth control are not always negative. Some have no affect at all. Check and use protection if you are told it lessens its effectiveness. Find out for how long after finishing the course of antibiotics you should use protection as well.
I'm really uncertain what kind of dentist would put you on antibiotics due to teeth coming in. It's considered wise to have as few antibiotics as possible, so it's avoided unless there are actual symptoms of a bacterial infection...
I'm confused here. You had unprotected sex while on a pretty powerful medication that can affect birth control... but you didn't say what type of birth control you are on.
Could you specify what type of BC you are on?