You're doing the right thing Ace.
I went through this with a cat I had for 16 years. At the time, I balled at the vets. Literally balled. One of the hardest things to do in life is lose a beloved pet.
After all was said and done and he was buried, I felt better. Now all I do is look back at the memories (which there are a LOT) and laugh at the funny times and things he would do. His personality. I gave that little guy a damn good life.
I'm sure you've done the same. But you're doing the right thing.