I've noticed you answering a bunch of relationship topics and I appreciate you're not just here to get your answer and run.
Reading this, my takeaway is that you actually should
look for someone. But not necessarily the way you think.
Your ex was not only your boyfriend. He was your friend.
So make friends.
Sounds hard, eh?
My fave way to do this (and I bet I'm older than you) is via MeetUp. Just search for stuff in your area and cross-reference it with whatever floats your boat: travel, camping, cosplay, writing, fitness, crafting, anything that works for you.
You'll see people, either in person or perhaps online because of Covid. Either way is fine. Laugh, chat, talk about your shared passion, whatever it may be.
These people may be the kinds of folks you normally never would have hung out with, e. g. not in your age group, or if it's online, far from your location, etc. All of that is 100% fine.
Don't like a group? Then leave it. You're under no obligation to hang out with a MeetUp group if it stops working for you.
I am suggesting this because one of the holes in your life is the social aspect of things. There are other people you can go to Arkansas with, or fish with, or attend rodeos. Find those people. Find that tribe, because that's your
About the romantic aspect of it. You're right that you should be more or less over him before you go looking for love. But you don't have to be 100% over him oh my God stake in the heart of the old relationship burn it with fire etc.
You just need to be able to spend time with someone else and pay attention to them without continually comparing them with your ex or wishing they were someone else. This may be earlier than you think.
And making friends (I keep circling back to this, because I think it's key) will give you some practice in that area. The part of you that realizes that it's rude if you talk about Dave (or whatever your ex's name is) constantly when your new pal Becky wants to talk about rug hooking (or whatever your shared passion is)? That part will tell you, in time, that it's rude to compare Dave to your new flirt, Steve.
So consider it practice. Training wheels, if you will.
Will you cry over him again?
The death of a relationship is a lot like a physical death. You mourn what was and what could have been, and you mourn the fact that you're not the same person. As Bob Seger sings in Against the Wind
, "Wish I didn't know now what I didn't know then."
In time, you'll start to realize that you don't miss Dave leaving his socks all over the place, or his critiquing of your early Xmas shopping habits (teach the rest of us your secret, oh wise one). And that when Steve smiles, it's like magic.
Replace the above names as necessary, and lather, rinse, repeat until you feel not just better but awesome.
As for your kitteh, I hope you'll be able to see him at some point, when contact wouldn't be quite so fraught. But maybe stay away for the time being. Give yourself a chance to heal.
You are a worthwhile person and good lord you deserve to be happy.