There are many things that could be wrong with your kitty. He may have blocked anal glands (which can be very serious) or tumors or constipation.
do you mean his anus is protruding, or is there swelling?
Good for you fro taking him to the vet. However if you are not happy with the diagnosis and recommendations of the vet you have seen, most definitely bring him to a different vet for a second opinion.
Could you post a picture of the area?
Welcome to petlovers, and please do keep us updated on how your beloved kitty is doing.
PS I recommend you stop letting him out at all. You can't know what is on the grass in your yard. If you want him to have grass, grow a little container of "cat grass" for him. You can find the little kits in most pets stores or walmarts, etc.