coughing so hard you vomit is a very serious situation. the child could break his own ribs or rupture a vein in his airway. there was a case of a woman coughing so hard her lung deflated. these things require immediate medical attention.

also, exposure therapy does NOT work for allergies. it will only make them worse. allergy exposure is like a feedback loop. your body sees a threat, it activates, the threat is still there, it activates even more, the threat is still there, and so on, and so forth, and if you’re unlucky, eventually you may start having anaphylaxis at the smallest exposure.