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
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Also found this which might be of help in the future.