At the risk of sounding hokey....I don't know about Airborne, but we've had great luck adding probiotic foods to our diet.
Truly, we stumbled upon probiotics by accident, (before probiotics became a buzz word) and stopped getting sick.
Yogurt is the best known, but avoid brands with thickeners. A variety of brands is best. We love adding orange juice and/or fruit. Greek cucumber dipping sauce is also yogurt.
More great foods include: sauerkraut, buttermilk, miso soup, any pickled foods: pickles, kimchi, kombucha, etc. Aged cheese is also good, like real Parmesan.
The other great news is that you can find at least some of the above at WDW! Miso soup is at the QS in Japan. Also, the seaweed they use to wrap sushi is off the charts in calcium!
Casey's (MK) and Epcot's Sommerfest QS sell saurkraut. Sanaa has pickled dips and paneer cheese.
WDW serves yogurt, but much of it is the cheapo kind. I think the only CL which offers plain yogurt is GF. Go figure?
One other Orlando theme park option worth mentioning is Citywalk's Menchie's. (self serve frozen plus toppings)