British Shorthair kittens & cats in Greer, South Carolina

This cat was found by our neighbor when he was a stray kitten. The neighbor took him in (and took his brother in) and kept him as an indoor and outdoor cat. The cat was never neutered and likely not vaccinated although I cannot be sure. The neighbor ended up moving and left the cat behind due to him fighting with his brother (because he is not neutered). Rather than getting him neutered and getting him vet care he just left him behind. We brought him to the humane society today but they were not able to take him due to a heart murmur that they heard. They said it could be due to an infection or something more serious like a valve issue etc.. They think it is likely infection related as he gets in frequent fights and has numerous open wounds right now, which are likely infected and the source of his murmur. I am in shock that they cannot do more for him and sent me home with him. We are not able to let the cat into our home due to allergy issues. He is SO sweet and loves belly rubs.