I have a lopsided and thin top lip. What are my options?

Obviously, the quick and easy solution to your problem would be the injection of a hyaluronic acid (such as Restylane, Juvederm, Belotero, etc.) filler into your lip to give it more volume as well as even out the asymmetry.  Also, if you don't like the result, it isn't permanent.  I would suggest doing this a week or so before your casting call to allow any bruising or swelling to subside.

Dear imugly (you are definitely not!):You have so many good things going for you with your lips that you should not have to do anything to feel confident in your casting call. However, to even your lips out a bit you might consider a very small amount of a hyaluronic acid filler such as Beletero or Juvederm Ultra injected in targeted areas of your lips.  With your casting call coming up, I would recommend you allow at least 1 week, preferably 2 weeks, for things to settle down, but if this is not possible, a more conservative treatment that can be topped up later can be considered.