I have a solid addiction going on. My character has now been drunk since I arrived on the ferry, I'm not sure it is much of a problem, plenty of booze around.
If I am remembering Fallout 3 right, doctors can just cure addictions. I could be wrong though it has been like 5 years since I played, and I exitted the vault and bealined straight to the ferry and point lookout.
So far, the only merchant I have found is the "House of Wares"; which offers general stock (including Aid), and also offers repair service. But no doctoring.
I'ld rather not pay the $450 to travel back to the mainland for medical attendion, and then pay $450 again to return to Point Lookout