Please advise if it's normal to feel sick four days after getting drunk?

It can be: After a severe hangover, but may also indicate that you have developed alcoholic gastritis, pancreatitis or hepatitis. I would see a physician if you are not feeling better after this much time, where a full history, physical examination and some simple laboratory tests can tell you what is, or isn't going on. And don't drink that much in the future. If that is hard, get some help cutting down.