What does Sinusitis do in a baby?

Your son probably is having difficulty having a bottle cause he can't breath through his nose which is what little ones do and the vomitting is probably as you said all the extra drainage going down and irritating his throat.. Try some sort of chest rub ointment like Vicks vapour rub or euky bear rub to help with the nasal congestion and offer the bottle frequently giving a little often will help keep him hydrated.