I know how you feel. I recently lost my beautiful ragdoll cat who was everything to me she was 16 years and so sweet in every way. We can only console ourselves buy knowing they had a good life and lived a good age. My thoughts are with you, time will heal.
I remember my 17 year old when i put him to sleep it was a very difficult first few nights sleep but then i started to feel less frantic. My second cat was put to sleep two months ago and was very very young, and that was torture, but i am beginning to accept what happened and how i have to accept things because i am powerless most of the time. I am sure your cat knew how loved it was.
I got another cat very quickly which i wasn't sure was the right thing to do but i couldn't cope with the empty house. My new cat is amazing company and has really helped comfort me. I feel like every time she does something funny, it reminds me of similar things my previous cat did and how much i loved her too. One big load of special cats.
I found out from the vets where they would have cremated my cat and scattered her ashes and went to visit. The fields were covered in poppies.