Is there some way to self host what cloudflare does?

Your domain will always have to be rented through a 3rd party. Cloudflare is (or was?) one of the better choices for that.

Cloudflare does other things as well, most notably it can acts as a proxy: an inbetween between your server and the users. This inbetween can be useful against DOS attacks, blocking of bots, etc. But for most self hosters that part is not necessary. It’s a toggle in cloudflare’s DNS dashboard: I think you’d want it to say DNS only.

Another thing cloudflare can do is tunneling. It’s useful for when your server is behind a firewall or NAT or double NAT you can’t or don’t want to configure. You’d probably know if you use this, so I assume you don’t?