I honestly think that you should believe that your old therapist had a full caseload. The first thing I thought when I read the first sentence of your post, was that there was probably scheduling issues or space issues. You should try to take this entire thing less personally. It most definitely was not your fault, and you can't change it, so you should make the best of the situation. You're going into therapy to get better, not to worry and feel hurt that you don't have the same therapist as you did before. I genuinely believe that it was not by the decision of your old therapist. You should give yourself a break, you didn't do anything wrong.
Good luck with your new therapist!