I understand this. When I was very depressed I spent a lot of time very worried about my dogs dying. I obsessed about it. I almost couldn't love them because I was so wrapped up in them dying someday. Once the depression cleared I starting seeing things differently. I wrote something about it to remind myself in case I ever get depressed again, or in case I need to read it when my dog does die. I'm going to link to it if you'd like to read it. I hope it helps you in some way.
Pet Loss: Finding Peace for A Broken Heart - Winterbritt