I haven't read through comments yet so I may be redundant.
Hey... So sorry. Pets are a personal relationship. That loss is a grief just like any other. It's hard because others don't have the relationship to that individual that you have.
Grief is something you carry through life. It isn't linear, but it does get easier. Grief will come in waves. You'll be fine and then it hits you out of the blue.
Do we just live and suffer and die?
Well, yeah.
But we also love, and get excited, and feel, learn new things, explore. We fall in love; we experienced heartbreak. We have moments when we notice the light coming through the leaves in the forest, or the sound of water on rocks in a creek, an interaction between a grandparent and young child, the smell of a newborn's head, that first time a cat settles in your lap, coffee when no one else is awake, the first sign of success in a new hobby, I could go on and on. So many things. Observations that have a visceral yet intangible emotional reaction. So so many things.
Let grief make you tender. Let grief remind you that everyone will deal with it in different ways. You can connect to others through vulnerability. Don't let it make you hard or resentful; there's so much beauty and love in the world. There's so much love in the personal relationship with a pet. There is love you can't describe.
Engage with the grief. Don't bottle or avoid it. Feel it. You're grieving because of the depth and complexity of the relationship. That's totally okay. That's healthy. It's gonna hurt. It hurts.
I'm so sorry you're feeling this right now. Take your time and feel it. Don't feel like you ever have to let that go. That's life.
Live, suffer, and die? Yeah, you could say that, but it's in the most beautiful way, and there's so much in between.
The depth of your grief is an expression of the deepness of your love. I promise the pain will subside, but it will take time. You will get through this. And your memories will give you a bittersweet comfort.