My heart goes out to you. Mold is a rotten deal. I'm sure the construction experts will give you some good ideas here.
To help with breathing, eye irritation, etc., I've bought some things and had good help from
www.nontoxic.com . I also have a UV air purifier from
www.airoasis.com and run HEPA air filters as well.
When I lived overseas my mother used to tell me that her shoes would mold in her closet. I couldn't imagine it. Now that I'm here, I leave my closet doors open.
I run a dehumidifier in the summer. I'm awaiting a parcel full of zeolite to help with the trouble as well.
I sure am sorry you have that to deal with.