Is there a connection between enlarged adenoid and food allergies?

Yes: It would have to be in the differential with the sx of enlarged adenoids.

Not directly: Many children with allergic rhinitis have enlarged adenoids. Many allergic children also have food allergies. But one problem does not cause the other. They are both manifestations of the allergic state.

No: Many kids have enlarged adenoids, and many kids have food allergies, but that doesn't mean the two are related. That is why adenoids don't shrink when parents carefully avoid all traces of food allergens from their child's diet. Adenoids don't shrink with treatment of either food or inhalant allergies; if they don't get smaller as the child grows, they may need to be removed.