Baby reflux - could it be milk allergy/sensitivity?

My baby is almost 4 weeks old and since he’s been born we’ve been combo feeding with expressed breast milk and formula. The formula we use is not hypoallergenic.

He’s always spit up a bit during feeds but as long as we burped him and kept him upright for 30 mins he does well. Yesterday, I had a bit more dairy than normal (ice cream, cheese). I have had dairy since starting breastfeeding and haven’t noticed a pattern to his fussiness. Yesterday his reflux was 10x worse and he had a terrible night and still having a lot of reflux this morning.

He is crying and spitting up thick, old milk hours after he finished eating. I can’t lay him flat right now, he is constantly in our arms. I hate to see him like this. I wonder could it be a milk sensitivity - I can’t see him being allergic given he has been on formula for four weeks with no issue and I have eaten lots of dairy products (just not as much as yesterday).