A poorly vented bathroom exhaust fan into the attic can it create mold in the house?

I had a rehab project done through the City of Orlando and they hired an incompetent contracting company Black Street Enterprise whose work was substandard. I recently discovered fine cracks appearing in my bathroom ceiling and became concerned. I asked another contractor I know to see if he could figure out why they were appearing. The ceiling had been painted and textured just a year ago (Not by Black street) He went up on the roof just to check and every thing was ok. He ask me if Black street had installed an exhaust fan in my 2 small bathrooms, I said they had. He said they had NOT put any ventilation as was needed through the roof to let the air out!.This means any moisture from the taking of hot showers was just being let out in to the attic all this time and he believed just recirculating back through the house. He also believed these pin line cracks in the ceiling were also the result of this moisture over time. I to seem have had chronic congestion, and sinus issues and infections, as well as chronic fatigue, memory problems, well as wide spread muscle and joint pain. My son when he is over for any length of time seems to have head aches. Even my cats sneeze! I am worried because of this improper ventilation mold is in my house causing these issues. Also I seem to have to high humidity and mold gets on different items including handbags, furniture, and there is sometimes a musty smell in the air as well as in closets.What ever is going on is effecting my health and even making it difficult to work. Please help! Is it possible all these issues are the result of this lack of the correct ventilation Black Street did? This one contractor who discovered the lack of the venting thanks it could be.