This happened to me on my last character, who had so many glitches I just had to re-roll.
I get what you're saying. I would draw back my bow (most of the time in sneak mode) and line up my shot, wait for the perfect time and release.....thud....the arrow drops to the ground. The enchanting/alchemy/armor improving tables also stopped working, I couldn't access them at all. Even with some magic skills in the 80's, the adept spells for those schools never showed up at the College. That whole character was a wreck because of glitches.
I started a new character and so far have not experienced anything worse than a bugged quest in Riften (small misc quest, so no big deal). So since you are still at a relatively low level, you might consider starting over to see if the problem carries over to a new character.
Edit: Also LOL at the guy below me
