Room and clubroom got me mixed up a couple times too. The (top to bottom) ground-private-dirt radicals are in both of them. Here’s how I concrptualize it: when I’m in my room, I’m constantly cognizant of the position of the roof (or the ceiling). The flag radical looks like a roof to me. It looks like the way I think of the ceiling when I’m in a room (it includes walls; the flagpole is the wall). And… ugh, the roof radical in 室, well it’s more like the roof/ceiling of a room I’m not in; I only see the top and it doesn’t surround me.
部屋 I think of as my/someone’s unique and personal room, and the 屋 kanji feels more personal to me than 室 which feels more generic. Especially because it’s used as a generic ~room suffix.
There’s always a slight difference in the radicals used, so paying close attention to them is your only option.