*big hugs*

I wish pets never had to die. I still now get pangs about Rufus (he's the orange-and-white cat whose icons I use when talking about departed animal companions on LJ -- I don't have the icon on DW right now), who passed away eight years ago, although thankfully they eventually started coming less frequently and became more manageable. But it was debilitating for a long time. Be as gentle with yourself as you can be while you're going through this.