What would my bedroom wall switch control if not the ceiling fan or outlets?
If both sides of the switch test as hot with the switch in either position, I'd give odds that the switch is supposed to control a half-switched outlet. What has probably happened is that someone replaced the outlet and didn't break the tab on the hot side. The result is that the always-hot side is also feeding the switched-hot side through the unbroken tab.

[Photo from another stackexchange post]
Check the outlet boxes, looking for a dual receptacle with both black and red wires going to the hot side but an unbroken tab. Breaking off the tab should fix the problem.