Hi!
I have had recurring, nasty bouts of mastitis (same cause) with this lactation--my fifth. The only thing that has helped is a combination of herbs (oregano oil, dandelion root, schizandra berry), iodine painting on both breasts (not on the nipple--haven't been brave enough to try that!--and, strange as this may sound, after doing some research I mixed up some anti-fungal essential oils (clove, oregano, lavender) in a sweet almond oil base (coconut would work well for part of it) and put several drops in my navel when I lay down to go to sleep. I have also rubbed coconut oil with essential oils in it on both breasts and eaten coconut oil which seems to help. I have been battling this alot recently, and the thing that seems to make the most difference is eating coconut oil, painting with iodine and dripping the oils in the navel....
I realize this may sound batty, but it's helping--I feel great for the first time in a long time.
For your baby, even at two months, you could dip the nipple of a pacifier or bottle into some organic baby yogurt and get a bit into him that way to build up his probiotics, which fight the yeast. Also, the coconut oil would undoubtedly help--I would try rubbing a little bit of it into his navel.
Best wishes and blessings--oh, and if your baby is throwing something up--I'd quit giving it--clearly his body is rejecting it!