Please Emily, it was NOT your fault. Don't get yourself all depressed thinking it was cause it wasn't. Blood clots are so unpredictable. I can relate to your loss as many others here can also. The best thing to do is cherish the memories you have of your precious Snowball.
Perhaps is you get yourself another kitty it might help ease the pain. I know it helped me.

Take care and I wish you all the best.

Rest in Peace sweet Snowball.