I was trying to re-caulk our bathtub, while pulling out the previous caulking, a piece of the wall ripped out. It's a small piece, about 1"x3", I believe the caulk was built up behind the wall, so it tore it out. I'm not sure what the shower wall is, which is part of the issue. It's a thin material, maybe acrylic? It is three separate pieces with seams in the corners, surrounded by a thin metal lining.

I'm not sure if it's possible to just fix the hole, or if replacing the whole wall will be needed. I'm looking for the cheapest method, but the best fix will probably have to work since we plan on selling the house in the next year.

Any help would be greatly appreciated!

So this is like a bath tub surround wall unit , right? It could be acrylic and probably not fiberglass since it would have splintered. You might be able to clean that piece and glue it back in but it will never be the same. You won't hide it from a buyer so just forget about it and absorb the possible lower offer on the house. Your other option is to replace the unit at your expense and then you have kind of messed yourself by paying the whole price. Who knows, the next buyewr may be looking for a fixer upper and would tear out the entire bath.