I think that considering that wheat and milk sets off your childs asthma really means that your child is allergic, as in classic allergy , not intolerance.
sadly if you have one allergy , you are more likely to have others.
However it may not be that your boy is devoping new allergies, its just that you are finding the causes of the allergies he has.
baked beans are legumes, and 5% of those allergic to peanut are also allergic to beans.
So obviously caution is required.
I would not intoduce any new foods until you have your appiontment at the hospital.
As for environmental allergies they do have a cross reference to food allergies, for instance , those with tree pollen allergy are more likely to develop fruit allergies.
Dustmite is a common allergy, and i personally develop swollen eyes if I rub my eyes when dusting ( I also get a burning sensation in my hands!!) But I am not food allergic.
My son has quite a high rating for dustmite allergy, and along with wooden flooring , good dustmite covers on the bed, and a nasal spray , we get by. ( he snores terribly!!)
a good book to get hold of is the 'complete guide to food intolerance and food allergy' by prof Brostoff,published by Gamlin.
my boy allergies at 5yrs were, peanut/treenut/all beans/kiwi fruit/ dog /cat/dustmite/eggs/tree pollen/hay fever.
at 11yrs, are peanut/beans/kiwi fruit/yeast extract/dog/dustmite/cat/tree pollen.
There is every chance your child will grow out of some allergies, esp as he is so young.
good luck with the testing.