I am so very sorry that your sweet kitty, Angel, had to be put to sleep because of illness. But what a wonderful 17 years full of memories you've had! :)
Please ask God to help you put those painful last memories of the last week of illness, and having to put her to sleep, out of your mind, and ask Him to help you remember all the good times you shared. I know it sounds corny, but God cares so much about you and your pain, and He WILL do that if you ask Him and believe that He is able!
Please don't feel guilty about helping ease your precious charge out of the pain and suffering she had at the last. She knew how much you loved her and that you wouldn't intentionally do anything to hurt her. My guess is that your crying might have made her scared, not the circumstances of being put to sleep. Pets are SO sensitive to our feelings!
Your precious Angel is playing in those grassy fields in Heaven with other angels, painfree and happy. I truly believe you will meet again on the Other Side. I also believe you may truly get some ADC's from her, as many here have had ADC's from passed pets, including myself.
May you find peace and comfort. God is good!