Do not worry, you can ignore it, because red eyes caused by hangover will fade away naturally if you have a good sleep. And you can take some milk or green tea to make you feel better after hangover. Or apply a bag of ice to help your eyes recover more quickly.
First you need to get as much rest as you can. It means you can wake up late. When you wake up, then take a cold water shower. The cold water can wake up you body, fresh your mood. You may also need some icy water. You can put a bottle of water into the refrigerator before you go to sleep. After you wake up, take the cold bottle and press it on your eyes. It can help reduce the redness of your eyes. Eye drops can be helpful too.
If you want your red eyes gone, you'd better stop parting. Go to bed early and don't stay out the night. So, in a word, give you eyes more rest, then they will be fine.
Well, it seems that you are allergic to alcohol. Since blood capillary is easy to see after stimulated by alcohol, and vessel will expand to a certain extent. So I suggest you'd better drink some honey water. Second you can drink some fruit juice, like orange juice, apple juice, and so on. These fruit juice can help you eject alcohol from your body rapidly. Then you can take a hot bath. In the end, go to bed and have a good dream. If those suggestion still can't reduce it, you'd better see the doctor.