I'm so sorry to hear of your loss, Lost Spirit. I think it's good that you can cry. I often think that men should cry more often. I know that for me a good cry can be cleansing. As to how long this should go on, and how often, that will work itself out.
I had a small black long-haired princess type cat who had cancer of the jaw. All she could eat (sip, really) was raw chicken livers that I blended. And I had her on an opioid pain killer. I remember I was writing a screenplay during all that, and she sometimes sat on my lap at the computer. Thanks to the opioid she was content. But there was this awful smell of rotting flesh, since the cancer was eating away at her jaw. Still, in its way this added to the tragedy I was working on.
.. I remember one day after she was gone.. (I too had to have her put to sleep).. but I realized I actually missed that god-awful smell since it was so strongly associated with my poor little dying cat (!)
.. so, yes, we get all bound up with these little creatures, and they do, as all here have expressed, give us a chance to give and love tirelessly.
Be well, Lost Spirit. You clearly have a generous heart.