There is a condition called litter box dermatitis, but normally the area that is involved is the skin around the tail and anus.
That red protrusion you are tallking about. Could you be seeing the penis itself, like in the pictures here?
Is your cat taking repeated trips to the litter box or showing any other signs of discomfort?
Sometimes when cats are in pain from a urinary problem, it looks like they have an erection. (Actually that's what it is but pain and discomfort are the reasons, not something else.) Normally when this happens the cat is also taking countless trips to the litter box at the same time, so the connection is very clear.
In dogs there is fairly common problem called paraphimosis, which is the inability to resolve an erection (in neutered dogs after masturbating for instance). The penis is stuck in an erectile condition and is very painful.
I don't know whether the same thing can happen in cats, I haven't heard of it myself.
Depending on what the sitiuation is by the time you read this message, the safest thing may be to call your vet for advice.