Guilt is a feeling and while we can acknowledge, learn from, and accept our feelings, we can also try to let them go. My t is trying to teach me how to let go of some of my feelings so they don't have such a hold on me and my life. Work in progress.

It sounds like you are taking good care of the cat. I've always had a pet cat in the house and it is sad when they die. I don't look forward to it. Loss hurts but it is one of the risks that comes with love. Sort of like a fact of life, I guess.