Where can I bring a wounded cat?

I just recently moved and there’s a old cat I’m feeding her. She has lots of wounds from itching. Not sure if it’s a sickness or fleas. But her wounds are pretty bad. You can see patches of her scalp.

If I’m (hopefully) able to catch her one day, where could I bring her?

Which shelter will help wounded animals and not put them to sleep?

Any advice is appreciated, thanks.

Update: I tried to approach him to take pictures of him, but he ran away. I don’t think I’ll ever able to actually catch him 😞