Most people would have red eyes after drinking and it will disappear after one night sleep. It is because when you drink your blood vessel dilate and you get dehydrated. If it is not serious, you don't need treatment.
The alcohol can make the blood vessels in the eyes become enlarged and dilated causing the white surface of the eye appear red. It is normal for people after they drink a lot. Some people have red eyes because they are allergetic to alcohol.
Maybe you are allergic to alcohol. If it is slight red, then there is no problem and you don't have to worry about it. If it is extremely red, it will do harm to your body. So you'd better drink less or not drink at all in order to keep you healthy.