I would assume that you need a dehumidifier on your heating and air conditioning system.

Good luck to you. On white linens, just use Clorox bleach when you wash them.

I second the need for a dehumidifier....close the windows and turn on the airconditioner.
And if comforter set is down filled, soak it in oxy clean...
But first of all dry your house out...open closets and turn the air on to chill!!
Linda c

In addition to the humidifier, if you haven't already, use Damp Rid in your house. The product comes in different types of containers for convenience. There's also a hanging version for closets. It appears you may need all the help you can get to get rid of the dampness. Hope you solve this problem fast.

I can give you a simple and green cleaning way of removing mildew stain from your linens. Simply mix vinegar, baking soda and lemon juice and apply this paste on the stained area. Leave it till the paste gets completely dried, then wash it off by rubbing the stained area with your hands. This will surely help.

I found the generic Damp Rid at the Dollar Store & it works great! I once lived in a house where the linen closet did the same thing & it was a constant battle. Just wish Damp Rid, ($1 generic equivalent) was around then!