Hi... I don't want to intrude, but....
I just read your post, and I wanted to say how sorry I am about Kiki. Please don't listen to anyone who thinks feeling this way about a pet is silly. They really don't have any idea, and haven't experienced themselves just how wonderful -& how sweet - it is to have an animal as a special member of your family.
Remember how much you did to try & help, & then, you helped her to not be in any pain anymore, when it turned out that her physical condition wasn't going to get any better. I believe you absolutely did the only right thing.
The same thing happened to us last year with our sweet doggie Audrey. It's hard at first, but I promise - it does get better. I hope you'll try not to worry about not having been able to actually say "goodbye": Kiki felt that love in everything you did.
Take care, & give yourself time.
A fellow pet lover, Selkie