My DD seemed to poo constantly and had horrendous nappy rash from 2 weeks old until 15 weeks .
I was also breastfeeding and had been told that pretty much anything was normal poo wise in a bf baby, so didn't worry about it.
Had loads of different treatments for thrush (for DD, not me!) and none of them seemed to work. Has your doc ruled out thrush?
Eventually I gave up eating dairy, and also had Nystan drops to give DD (yet another thrush treatment), and that week her nappy rash went and hasn't returned. I don't know if it was the dairy or the Nystan that did the trick.
She also stopped the constant pooing, which was in fact cause by a dairy intolerance (reasonably common in babies).
I would recommend going back to your doc and asking him to explain what makes him sure it isn't thrush, or getting him to give you treatment for it, and/or giving up dairy for a couple of weeks.
The symptoms of dairy intolerance can be many and varied, but if your DS has no other problems then I don't want to worry you overly about this - with my DD there were clearly other issues too.