Most people have moderate allergies to every kind of mold. As PP suggested if you do not know what you are dealing with it is best to contact a professional. Stachybotrys or black mold can be deadly.
I have a good deal of experience with cleaning and mold remediation and the thing is without knowing the source of the moisture it is impossible to say what effects it could be having on anyones health.
Bleach kills mold so does sunlight or UV light but without getting rid of the source of the dampness it will just keep coming back. the do sell dehumidifiers relatively cheap these days which would also help.