The leaf mold happens after a killing frost, when the sun warms things up during the day. If he kicks through leaves (what kid doesn't?)- bingo, he's kicking up leaf mold spores. And tracking them in on his shoes. Another few weeks and the leaf mold will be over for the season.
You have forced hot air - when were the filters last cleaned/replaced? As to there seeming to be no difference between inside and out, etc., once your histamine level is sky-high (which is what happens when you are having an allergic reaction) it takes quite a while for anything to effect a change, good or bad.
Do get him tested, it will be good to know, one way or the other. And if it is allergies, well, that's not a bad thing - there are ways to deal very concretely and specifically with allergies, as opposed to trying to fight an unknown!
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