Yes, drinking can cause itchy eyes. Excessive alcohol drinking can cause symptoms such as increased sensitivity to medications or alcohol, vomiting blood or blood in the stool, and intense itching. Actually, even if you just have a nightcap in the evening, the alcohol you take in can rob your body of nutrients and cause your sleep to be unrefreshing and poor quality. And it can also exacerbate rosacea and cause red watering eyes and broken veins on your cheeks and nose. In fact, regular drinking will suppresses the immune system and makes you susceptible to infections. And all those conditions will cause eye itching. Sometimes, touching your hands and fingers to your face often without washing them can also make your eyes itchy, because it will transfer a little grime and dust to your eyes.
So if you want to relieve eyes itching, try to stop drinking and do not touch your eyes with dirty hands. If it don't get better, go to see your ophthalmologist.