Sorry to hear that. I disagree though with killing sick pets. I think it is inhumane to animals and you should treat them like you would people. Would you kill a sick relative with a lethal injection for a crime they didn't commit?
yaacov, i disagree wtih you half way. With a sick relative, you go in accordance to Judaism by erring on the side of life until proven otherwise by a Rabbi.
With an animal, I believe you err on the side of its death. Animals kill each other on a regular basis due their nature and lack of soul (that is a soul that mimicks one of a human). As human beings we should be humane to Gd's living creatures and therefore take care of them while they are healthy and alive and end their lives humanely when they are sick or a danger to other human beings.
And yes, I can't stand the sight of a suffering animal especially a mammal especially a pet one has raised and grown up with..and i'm sure there is a place for their cat or dog souls to be..but it's for Gd to also determine and for us not to worry about. The death of a loved human one and loved pet one is part of the circle of life and part of our soul's growth.