Newborn baby sharting constantly....

My 2wk old is having poopy farts/sharts literally all day. He will have one or two more substantial poops in the day (more than a tablespoon) but then will leave smears in his diaper every time he parts- which is alot. He is breastfed and the color is the healthy deedy mustard brown/yellow, but the frequency is causing him to have terrible diaper rash.

Had anyone experienced this? Will he grow out of it or is there a dietary issue i need to think about? I don't consume much dairy.

UPDATE: Thank you for commiserating and sharing your advice, everyone! We've been using the peri bottle rinse and air drying before slathering on aquaphor and butt paste, and it's 80% better already!