If he's got a yeast rash (most likely due to abx), but you don't have it on your nipples etc, then I wouldn't say you have to give up yeast products. Eliminating dairy, if you feel it's a likely source of intolerance/allergy, is your best bet. It's really hard (I know, BTDT, twice), but worth it if you see major improvement. But if he doesn't seem to have other symptoms (gas, colic, reflux, skin symptoms, etc), then I don't know--I wouldn't stress about it too much, esp since the rash you've seen lately is mostly likely due to his cold or teething. Soy or rice icecream aren't bad, actually, and soymilk (if he's not also sensitive to soy) is a decent alternative to milk in coffee etc.
To get rid of his yeast, give him loads of probiotics, add apple cider vinegar to his bathwater, and olive (etc) oil with tea tree oil makes a great anti-fungal diaper swab (just a couple drops TTO, though: it's strong stuff). You can sprinkle probiotics directly on the rash, too. Coconut oil in his food (if he's old enough) is a good antifungal and gut healer as well. You can take probiotics too, and he'll get some benefit.
If he's CD'd, wash the diapers in really hot water with vinegar or TTO added to the rinse cycles.