Lurch into the hospital's emergency department and look around for something called the Patient Bill of Rights. You will discover that you will be treated, in an emergency, regardless of your ability to pay or your citizenship status, although if it is a fairly small wound you could always try to look up an Urgent Care center instead.
Whether or not you're a long-term resident, I rather doubt the hospital or clinic will care overmuch, being as how they're generally staffed (in the seeing-of-patients area, at least) by people who actually do prefer to keep other people from bleeding to death, yea even unto not being paid.
Alternatively, I can't possibly be the only person around here who has enough spare funds temporarily to send the can 'round and cover a patch-up job for you.
(And in case anyone gets the idea that that means they should rob from me: I was awarded grade 9 in sabre, I still have it, and I have an Irish wolfhound. Just so we're all clear.)