This does not sound normal.  If your lip is still numb, and or swollen, then perhaps it's time to see a doctor.

If you are making your lower lip sore you are probably biting, which is not good embouchure technique.  You might be using a reed that is harder than what you are currently able to handle, resulting in biting.  The lower lip should be relaxed and resting against, but not over, the lower teeth, as in saying the letter "v."  There are Youtube videos on embouchure technique featuring the great Joe Allard, which I found very beneficial.