Bubbly paint reveals a host of problems

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Q: Last winter, the interior walls of a corner bedroom occasionally bubbled out as if water was gathering on the other side of the paint. This usually happened after a good downpour. I just checked that corner of my flat roof and discovered that a neighbor's overhanging tree had clogged the corner drain and downspout with leaves and soil-like detritus. I asked the neighbor to trim her tree and she did. But it seems the branches grew back more quickly than we both thought they would. I can clear out the corner drain and downspout as a spring project. Next fall, I'll be sure to trim the overhanging branches myself if her gardener fails to do so. But it seems as if there's still some water lodged behind the bedroom paint. How do I get that out or will it dry on its own? Also, should I be worried about water damage or dry rot? If so, what would you advise I do? Interestingly, there are no water bubbles breaking out on the outside paint. A: Flat roofs are notorious for leaks at drain spouts...