Sounds like a bit of a mental misfire. Malted milk is a dairy product. Malted milk balls are typically made with milk chocolate. But barley malt and malt extract are, as far as I can tell, not related to dairy products at all.
It's possible that these pretzels are made on equipment that also manufactures dairy product (e.g., cheesey pretzels).
One indicator of this is if they're labeled kosher-dairy (typically, a U with an O around it, followed by the word "dairy"). Most pretzels that I'd seen are "kosher pareve" (U-O with the work "pareve"), which means that they contain no milk or meat prodicts and they're manufactured on equipment not used for dairy or on equipment that's been cleaned according to the Jewish laws of Kashrut (laws about keeping foods kosher and properly labeled). As long-time readers can tell you, a "pareve" labeling is not an absolute guarantee of a lack of contamination, but it's as close as you'll typically come to  an indication that an attempt was made to clear the machinery of dairy.
Rule of thumb is this: if it hurts to do something (and that something's not essential, like breathing), then stop doing that something. If you consistently observe symptoms after your child has ingested something, he probably shouldn't eat that thing (same caveat as breathing, though). Since there are so many variables, you may want to retest your hypothesis a few times (stop, though, if subsequent reactions are worse). And you might want to watch for similar reactions to other foods containing any of the same ingredients. Also, look at what your child eats, drinks, etc., with that food, to see if it's an accidental association.
With a 17-yr-old son with multiple life-threatening and lesser food allergies/intolerances since birth, we've learned that detecting "the culprit(s)" is a very complicated business. The real trick is to keep them symptom-free without starving them. So far, my guy is doing pretty well.
Good luck,
Mark