About a little over a month ago right after my period I had unprotected sex early in the morning. And that same day I went on the depo provera for the first time. Could I be pregnant? My boobs are getting bigger randomly and I have been having funny feelings. I am not sure if its just the birth control or not.

Most likely it is due to the depo provera which alters hormones.
No birth control is 100% effective, so pregnancy will always be a slight possibility.
Try a pregnancy test. If you became pregnant at that time, it will most likely show up on a urine test by now.