The behavior of a black hole mirrors the behavior you'd expect of a two-dimensional object.
'Two dimensional object' is a contradiction in terms. If it can be called an object at all then it must have at least 3 spatial dimensions. Even an object only 1 atom thick would have 3 spatial dimensions. One of those dimensions would just be very small.
Whether something can have more than 3 spatial dimensions is pure speculation. It could be argued that such an idea is non-falsifiable. The whole concept of perpendicularity seems to break down when applied to a 3 dimensional (aka real) object.
Maybe we're in 2D space.
If 3 spatial dimensions are not required to measure our bodies then we do not exist at all. Even one atom thick creatures would require 3 spatial dimensions to measure. Also a 2D universe would not be a universe at all. A universe, by definition, contains everything that exists. A 2D universe could not contain 3 dimensional objects.