Hi there!
You are perfectly fine! Birth control is horomones, and your body will take a few months to adjust. When you are on the pill you don't have a "period" you have what they call a withdrawl bleed. So, your body is just adjusting to, and getting used to the extra horomones.
Good for you, using a condom. You really should your first month and after that you are protected as long as you follow the guidelines and take one pill around the same time every day.