What pill are you on?
As the above poster mentioned, condoms are a must for the first month when it comes to most birth controls so you could get pregnant. Sperm can live in your body for a few days, and some women are fertile as early as 7 days in their cycle. I'd suggest continuing to take the birth control but use a condom from here on out. If you don't have your period when you get to the placebo pills (it takes me about 3 days after being on those to start my period), then take a pregnancy test. The baby isn't as easily affected by most things early on in its life, so don't stop because of that concern. However, do not start the next pack if you don't get your period and find out you are pregnant for obvious reasons.
The following month (after the placebo pills), you may be fine to go without a condom, depending on the pill AND if you take it consistently, meaning every single day, preferably at the same time each day (and some pills are sensitive enough they HAVE to be taken at the same time; find out which yours is) for maximum efficacy. I'm on Microgestin Fe (purple pack), and I set my cell phone alarm so I take it at the same time every single day. My boyfriend and I have had sex for over two years without any incident (I'd started taking birth control long before then due to my period being debilitating).
I would consult your pharmacist, advice nurse, or doctor before simply assuming it's ok with your pill, though. And remember there is always a small percentage of a chance that you could get pregnant even taking it correctly. It's extremely small, but people have gotten pregnant on the pill. If you are not ready to face the possibility or are unable to consistently remember to take your pills, I'd use a condom in addition every time no matter how long you've been on it.
When starting the pill for the first time, you're supposed to use condoms for the first month, or at all times as a back up because the pill isn't fully effective until after a month of use. So pregnancy is possible. That being said, you'd just finished your period so you're not exactly in your most fertile time (that wouldn't be for another week or so) so chances are slim.
It's not good for your body to start and stop the pill, so I would keep taking it. Maybe an idea to use condoms as well here on out.