I agree with using Florastor or S. Boullardi (Florastor contains S. Boullardi) since it is not killed by the antibiotic and will "take up space" in the gut and keep pathenogenic strains of bacteria from getting the upper hand (this is likely causing the diarrhea). S. Boullardi is transatory. It does not populate in the gut, it just is there while you're taking it. You need to add in a probiotic with good bacteria strains in order to repopulate, while you will need after the antibiotic. A good probiotic acts just like an antibiotic and can shove out the bad bacteria.
Your GI tract is all one big piece, from your mouth/nose/throat down to your anus. Bad bacteria that are in the intestines can make their way all the way up to the mouth (causing increased suseptibility to cavities) and then it's an easy jump up the tubes at the back of the mouth to get into the ear canal to cause ear infections. It's a viscious cycle of ear infections and antibiotics. I had this growing up.
I think its wonderful that you are thinking of probiotics for your son, this can be SO HEALING. The most powerful probiotics are food-based ones, such as yogurt, kefir, and cultured veggies (saurkraut). They make it further down the GI tract and can do the most good at repopulating. It helps to take them with meals, for aid in digestion (giving some good bacteria with the food helps to keep the bad bacteria from feeding on it) and also in between meals, to repopulate the gut. The normal advice for probiotics is to start very slowly with small doses but if he's taking an antibiotic, his need and tolerance may be quite high for probiotics. His stools should improve when he's getting enough probiotic.
So just to be clear I would do BOTH Florastor and also a bacteria probiotic I really like VSL (prescription).