Flat roof, vaulted ceiling, too thin, too hot, moisture

Hello, please help!

    My flat roof portion and low grade roof portion recently had mildew or mold come through into my front room wall and ceiling. The beams showing on the ceiling of my front room are the structural beams. The low grade portion of my roof is vaulted ceiling inside. [They are both too thin, I think.] Since I had to take down a big shade tree, I got a new a/c central air unit (venting is below house in crawlspace) and new hurricane windows. But without the shade tree, it gets too hot in here in the peak of the summer! 

    During the hurricane that went up the coast but stayed out in the ocean, when we had all that heat, humidity, and rain, is when the moisture came through and mildew/mold appeared. I went up on roof when it had a break in the rain, and there were puddles on my flat roof portion. The decking felt soft when I walked across it. The area where the flat roof meets the low pitched roof, has a gully/low area along the length of the meeting of the two roof types. I flex sealed the heck out of it! It's holding for now, but I need a long term fix. Please Help!

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