If I'm reading your post correctly, you put a collar on a cat who had never had one before, then immediately picked her up. If this is they way things happened, then it would be pretty apparent that she was upset because of the collar. It's too late for Jazzie now, but maybe you can understand her better if you know that cats feel like something has "got" them when they wear a collar or harness. In other words, they think something has caught them and is about to eat them. Most cats eventually get used to collars and harnesses, but you have an excellent chance if you start when they are very young.

I'm sorry she hurt you, and I hope she doesn't do that again. But understanding the way cats think goes a long way towards understanding why they do the things they do, and how better to handle them.

If you get another kitty, start the collar early!

With Jazzie, keep the collar on her, but if she seems the slightest upset by it (ears back, tail twitching, snarling, growling) then stay away until she settles down. If you must handle her, wear thick gloves.