Drying up the house is a really good idea.

Possibly you could make yourself an area spray using a decoction (in alcohol, I think) of one or more of the herbs known for antifungal activity. Sage might work, but there could be better ones.

Spray the areas that smell musty. Avoid the areas you spray until the mist dries. Do not inhale it. (I always hold my breath when I use sprays).

If you use plastic bags for storage, they can hold in moisture and cause areas they rest upon to get moldy.

Especially check the closets on the north side of your house, and areas in your house shaded by large outside shrubs and vines.

If the drainage from your house's downspouts is not good, there are extenders that can be placed on them to release rainwater further from your house's foundation.

Only ventilate your house when it is cooler outside than in.
Warm air is able to hold more moisture than cool air, so warm air coming into your house will deposite moisture as it cools.

Get as much light and sunshine as possible into areas that could be musty.

tea tree and thyme are the classic anti-fungals...

but nothing but removing the spores will stop the reaction.

start by changing the filters in your air conditioners, and anything else that has a filter.

adding a handful of crushed thyme to a weak bleach solution will increase its mold and ick- killing factor.

vacuuming EVERYTHING with a HEPA-filter vacuum after it dries is a MUST. molds grow in damp conditions- they SPORE when it dries out, to assure that 'something' survives to start another generation. so sucking up those spores is just as important as killing as much of the mold as possible.

honestly, that's what made my bratty choice to buy a Dyson for our anniversary sensible- between my cat allergy (we have four) and both our mold issues, the WASHABLE filter on the Dyson gives us a fighting chance.

there is a homeopathic remedy called "mold, yeast and dust" made by Bio Allers. It works for me and my friends go to www.bioallers.com for more info.

One of the best things for allergies I have tried was to
stop eating food with sugar in it. This improves immune
function considerably. Also take vitamin suppliments. There
are 150 known species of mold that cause allergy as well as
some 50 known pathenogenic molds. The best way to deal with
the problem is to improve your immune system so that it is
less inclined to allergic reactions. Adaptogens help.

Two things come to mind after reading these good suggestions. In Traditional Chinese Medicine, the portal to the lungs is the nose and airways. Weakness or dampness in the lungs can show as runny nose and sinus congestion. You might want to look at a Chinese formula for the lungs. Individual herbs might include fenugreek or immature orange peel.

The other is that there is a new product combining luteolin and rutin, both flavones, in a lozenge. I have seen it do well for head and throat congestion. It is acting primarily as an antiflammatory. The mouth is a good place to absorb some molecules that otherwise do not come in well or get deactivated by the liver in a "first pass." The liver adds a sugar to these normally and that deactivates the molecule.

If you can quiet down your tissues, you still need to deal with the source of the irritation. I think that has been covered previously.

Richard

Drying out a house does not work. I live where it is 15% or less humidity in the summer and have a severe mold problem.
Not that I recommend spraying a whole house, but cold chamomile tea is an excellent antifungal.