I have a patch in my arm pit that looks like ring worm. Can I use a pramoxine hydrochloride cream to treat it?

You can do anything you want. Whether it will be effective isn't something I will comment on.

It would be best to talk to a doctor to make sure that is what you have. It might look like a ring worm but could be something completely different. Best to get a proper opinion of it before you do something about it.