That person lied. Birth control does not prevent implantation. Birth control prevents OVULATION.
You could definitely be pregnant. Starting mid-way in a pack isn't really a smart idea since many packs have variable hormones etc...
What you need to do right now is STOP having sex. Do no take any more pills. Next, you need to wait two weeks past the date when you had sex last, and go buy a pregnancy test. Use it obviously, and find out of you're pregnant or not.
After that, you'll either deal with the pregnancy in one of three ways, OR you won't be pregnant. Even if you get a negative result, I'd personally wait until your next period comes to be sure. Yes, more abstinence.
Once you are absolutely sure you are not pregnant, go to your gynecologist and get a prescription for a more long-term kind of birth control. Something like the ring, the patch, depo, implanon, or an IUD (yes you can get one with no children). Pills clearly don't work well for you as you do not take them.