The writing was on point, I think you really nailed the comedic style. My only criticism is that the timing is way off. Your short goes too fast making the jokes less effective. Also, the voices and animation weren't up to standards, but I can forgive that since it wasn't the reason I watched the video.
Overall, this was one of the better South Park fan animations I've seen. You should be proud! My advice is to study South Park's pacing if you ever do a second attempt.