After

"After + negative" is not used in English. "Before + negative" is sometimes used in a threatening kind of way, for example:

Mom to child: "You'd better be good before I don't take you for ice cream."

"You'd better study before you don't pass your final exams."

Taka

Would "after/before+negation," such as "after I don't smoke," would work fine?

Not in general. The negative does not mark a point in time, which is required after "before" or "after".

e.g.

Before I stopped smoking, I had a persistent cough.

After I stopped smoking, the cough went away.

There are few very odd cas