S.T.
I also had mastitis when my son was about 2 months old (by baby is now five months old) I have one breast that produces way more and gets engorged quickly, so I worry about it constantly. I've found that so far just making sure to not skip feedings and pump every 3 hours like you're doing is fine. But sometimes I also have to pump at night, if it wakes me up because it's painful -- then I pump. My baby has been sleeping through the night pretty constantly and it seems like my body is adjusting now. So I would suggest just to listen to your body, if it hurts and wakes you up in the middle of the night, then yes pump. I think your body will adjust.
But don't just ignore engorgement because not only does it hurt, but yes, can cause back-ups and infection. so I would pump after your son eats in the mornings to make sure you're empty because your milk supply is so much higher in the mornings. I do this anyway just to bolster my freezer supply!
no fun, I feel your pain, good luck!