Definitely go for the probiotic!! My son had acid reflux and yeast rashes when he was little (1-5 months) and the probiotic helped. We use Jarro brand acidophilus for babies. It's powdered, has virtually no taste, and you can add it to food, milk, or let them suck it off of your breast or finger.
He has never been on antibiotics, but I would definitely put him on daily doses of the probiotic as soon as I knew he needed the antibiotics.
It's also a great idea for you to get on the probiotics. If he has had a yeast rash in the past, then he could easily pass it on to you, even if it's not obviously in his mouth. My son and I passed it back and forth for months even though he never showed any symptoms in his mouth.
For the yeat rash on his bum, what worked best was using just water to clean up and an anti-fungal cream (over the counter--lotrimin) a few times a day.
Good luck--I know it's tough to have your little one be sick.