Drywall is a bad substrate for essentially gluing heavy stuff to. It's soft weak gypsum with a facer of laminated paper that can peel right off. If you really want a brick wall inside, I'd recommend just building it right in front of the drywall. Obviously, the sanity of this idea depends on several factors, one of which is the subfloor. If you're on a concrete slab, then no sweat. Doing this on the second floor or above a basement is another story.
If that's not an option, you could probably remove the drywall and replace it with cementboard, and then mortar a thin brick veneer to it like in that other answer.