As a pet loss counselor and from my own personal experiences with grief, I know there is nothing wrong with you. I also believe that the overwhelming waves of grief or gnawing emptiness will eventually diminish and the edge of the pain will soften.
It may not feel possible, but one day you’ll be able to talk about the animal you loved so much without crying or holding back tears. You’ll be able to remember the smart, loving, and funny things your pet did with a little sadness but also a smile, instead of only the acute pain of loss.