I got a cavity filled a week ago but now my tooth is sensitive. how long till it goes away?

Can take 4-6 weeks: It depends on how deep the cavity was, which tooth, what material was used--many factors.

It shouldn't be.: Your tooth should not be sensitive after the filling is done. The problem could be the bite or occlusion, some small opening or gap, or a problem somewhere else in the same tooth. Please call your dentist and he/she should be happy to see you and solve the problem.