Visible molds and mildews are a trouble.  Do you have carpeting?  If so, was it replaced after flooding?  Carpeting is allergen central for those of us affected.  Besides hiding mold in carpet and padding, carpet is a dust mite superhighway.  Mites love humid spaces.  Are you renting?  If you do have installed carpeting, find out about that and get rid of it if you can. ($$$$$$$$$$!)  Hepa filter vacuums are helpful ($$$!).  If you think mold is the main culprit, invest in a hygrometer (cheap) and a dehumidifier ($$) before investing in a hepa filter (more expensive to run due to filters, but some insurance covers X number of filters per year).  Turn on kitchen and bathroom fans RELIGIOUSLY, and dry out the tub and shower after use. Â
   Bedrooms are the next priority.  For all environmental allergies, washing all bedding in the hottest water you have (don't stress about hitting the official 135 degree mark), then in the hottest dryer at least every two weeks can have amazing results.  We send blankets through a "quick" cycle without soap to save money.  Put pillows through a hot drier frequently.  Keeping the bedroom pretty spare, if you can, keeps it a safe haven.  Store dirty (and possibly wet) laundry away from the bedrooms, and wash towel loads more frequently, even if the load isn't completely full.
   Throwing open all the windows for 5 or 10 minutes every day helps with all allergies and could alleviate possible chemical sensitivities.
   And watch for signs of allergic asthma, which can potentially become more acute as they age.  This is the worst-case scenario (besides pneumonia, of course).
   PHEW!  It sounds overwhelming, but soon becomes routine, especially since you will read and hear the same advice over and over and over.
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   As for food allergies, if they are present they have HUGE consequences compared to environmental allergies.  I am a big fan of allergy testing, as it can take away the guessing and waiting.  That said, kids aren't usually tested for things like oats and rice, unless you ask, and in this way I lived with an undiagnosed oat allergy for decades!  Occasionally skin testing is spotty or a complete bust.  And, without insurance, testing is expensive.  (Even with, sometimes).  It also is not an absolute substitute for elimination diets, but most of the time it does help focus the effort in the right places. Â
   I always give this advice: don't ignore uncommon food allergens (I am allergic to all grains BUT wheat) if you still get suspicious symptoms after eliminating the really common allergens.  And look for less expected symptoms: unusual lethargy, heavy mood swings, anger issues and violence in kids.  These are ones you can observe in kids and can result from these symptoms: confusion, adrenaline rushes or panic attacks.  (This all can look like a sugar meltdown.  DON'T necessarily dismiss tantrums as age appropriate.  You know your kids.  If you suspect a tantrum is food-related, it probably is.)  Listen for tummy aches, belly aches, too-stiff or frequently loose stools, and coughing.  The older ones will begin to tell you about their experiences, which will be a relief to you. The younger ones will still be watch-and-wait.
   Sometimes, after one culprit is eliminated, you can see symptoms from other allergens more clearly.  Some items might need to be eliminated absolutely, others less so, and even allowed on a limited basis.  (Our house, DD's main allergies are wheat and dairy, and all nuts and peanuts, fish and shellfish.  These are OUT.  Corn (hard to eliminate) luckily is not as bad.  The occasional baking powder or powdered sugar, or sprinkles can be OK.  Even a handful of popcorn once a week).
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   Finally (yaaaay!  Sorry this is so long.)  with the possibility of three kids allergic to different things, BE PREPARED TO BE A SHORT ORDER COOK.  Dismiss the notion of if-you-don't-eat-what's-for-dinner-you-don't-eat.  Do that, and you'll save a lot of headaches.  My best advice is make lots of plain food that can be chosen from.  Fry up a pan of onions for the adults to mix things together, put a block of cheese on the table for a last-minute grating.  Bacon is nice, if you eat meat and don't have pork allergies.  Organic Valley brand bacon also gives a lot of grease for dairy-free frying and adding to a pot of beans.
   One point of light:  if you had any really dangerous, scary food allergies, you'd have seen them by now.  So while what your dealing with is big, don't sweat it.  Like traveling by plane, the roughest spots are at take off.  Cruising altitude is easier.