Alcohol is a vasodilator, so your veins get big when you drink, and inflammation occurs.
Inflammation is itchy.
If it is a pretty strong localized itch every time you drink a bunch of beer though, it might be good to get that checked out. There's a thousand other intersecting conditions that alcohol consumption could be interacting with(or not be, so talk to someone with an MD), but that is not a common, acute or severe enough condition to get an undeniable answer, or probably even a close approximation, here.
Better hope it's not Alcoholic Neuropathy, the death of nerves in extremities due to alcohol use. Chronic alcohol use can make the damage permanent and the sensations will never go away.
Im no chronic, on average two drinks a month I'd say. its probably the inflammatory answer for me, but I appreciate learning another frightening fact about our bodies!
Drinking alcohol can increase your blood pressure, and a symptom of increased blood pressure is tingling in the extremities.
Gluten allergy doesn't always give you diarrhea @spasm01@lemmy.world it could just be slowly driving your immune system into constant overdrive which then attacks things like your digestive and nervous system.
Go see a doctor.