I haven't heard of using an antihistamine or allergy shots to prevent asthma.
I have. Our research-hound allergist first suggested this to us when DD was about three, so almost a decade ago now.
This has been an area of clinical research in hyper-atopic kids for some time, actually... it seems to prevent subclinical airway impairment from resulting in airway remodelling that leads to frank asthma over time, or at the very least, in reduction in the severity of symptoms.
It takes pretty high doses of antihistamine to act preventativelty this way, but in most kids those second gen antihistamines (like zyrtec) are REALLY well-tolerated and they are also (pharmacologically) very very clean in terms of action and specificity. They hit histamine receptors and pretty much nothing else.
They're also old at this point, and seem to have no long-term side effects when given in children, even for decades.
That certainly CANNOT be said for asthma drugs.
I view daily antihistamines and allergy immunotherapy as two of the only
real things that we CAN do to help our kids-- other than avoidance, I mean.
Allergy shots really changed DD's life completely, even though it was a long and grueling process (6 years). She uses her rescue inhaler a couple of time a YEAR now, and when she started shots, she literally couldn't play outside for about four months of the year. She was on a trajectory to have pretty severe asthma by this point in her life, and, well--
asthma DOES still kill people.