I doubt if you'd get Antabuse from a walk-in clinic but I think you should try, and let us know what they say.
As Tetrax said above, medication that can help with addiction should be much, much easier to get than it is.
They all me Antabuse can be hard on your liver, so the prescriber might want to check baseline liver tests before starting you on it, to make sure it won't be making your health worse. Whether they do things like that in a walk-in clinic, I don't know.
If you do give it a try, please report back.