Even though you could be pregnant, it's a little too early to be experiencing these symptoms of a pregnancy if you think you may have conceived on December 1st. I do not think that a pregnancy test would help you this early on, but it doesn't hurt to try one of course. It is hard to tell when you are on a BC plan and just starting it out, and it could be playing with the timing of everything.
Birth control is only effective about 99 percent of the time if you follow the directions, so it is possible that you could be pregnant whether you were careful or not......and you weren't of course.
The symptoms you have could actually be side effects of your pill. If the pill is making you uncomfortable, maybe you should talk to your doctor about an alternative.