Most of the rings which come with straps (you can buy just the rings, just the straps or the rings and straps) also come with latches. These allow you to throw your rings around any rack/pullup bar/beam/etc
Just pay a bit extra and buy a reputable brand so you don't get shit latches that slip/ warp/break (some come with plastic latches, I'd make sure you get steel but that's just me, some folks are happy strapping down hundreds of kgs with plastic latches). I'd also recommend wooden rings.
It's also worthwhile getting straps which are marked so you don't spend a bunch of time trying to level the rings to the same height. Or if you plan to mostly set them up in the same spot, you could just mark them after you are happy with where you set them for the first time but that always seems to wear off.
I'd also make sure you are fully extending your arms (elbows and shoulders) and the bottom of the movement, without this your elbow woes will just reappear.