Even if your pet wasn't a rescue remember all of the good care and love that you gave them. If it hadn't been for you, perhaps they might have ended up living in terror and suffering at the hands of a monster or wandering the streets as a suffering stray. For some all of this can take a long time to sort out, for others, not so long. Thus, in the immediate aftermath, because of the suddenness and possibly traumatic nature of our pet's death, we are devastated. Or, we may wonder if something is wrong with us.
Healing takes time.
Our relationship with our pet was sincere and the bond complete. Perhaps though, the nature of our grief changes over time. And that's when we begin to find some measure of peace again because we know that we can never forget them anymore than we could forget our heart. They are one and the same. The following books are highly recommended.