I've had to put down two dogs within the past year, and it is very, very hard! I talked to my T about it both times, and even called her before I took the dog to the vet. It's an incredibly difficult thing to decide to euthanize an animal, especially one that has shared your life and your love. It's not something to be taken lightly and it's not a failure to need your T's support in this.
I'm glad you called both your T and the vet. If your cat becomes worse, you might call your vet back and ask if they will do a house call to euthanize. Some will. I know mine probably would.
I'm so very sorry you're facing this with your cat.