Four questions. No signup. If it's active, I'll tell you what to do in the next hour — for free. I'm an independent inspector, not a contractor.
Ring-shaped stains that keep growing after rain almost always mean water is still finding a path — usually flashing, a nail pop, or a crack you can't see from the ground. A cool/damp feel with no growth usually means the drywall absorbed old moisture that hasn't dried. Bulging = trapped water. Poke it low and let it drain.