Well, if you want the most potent, medically available pain killer it is a substance called fentanyl. It is a synthetic optiate that is usally adminstered throught a transdermal patch, or through an epidural or intrathecally.
It is so potent, an amount that fits on a pin head would kill you.
But to answer you question, opiates, like Vicoden, Oxycontin, Dilaudid and others mentioned are not recommended for managing your type of pain. They can be used post-op or post-procedure to manage acute pain as you heal, but you should not depend on them to help you excercise. I think the Motrin/Advil/ibuprofen or any NSAID would be a better way to go. These also help manage inflammation.
Sorry you are in pain, but you don't want to add an opiate addiction to your sore wrist problem. PM me if you want more details. I have some experience in pain management and related drugs.