It isn't just the alcohol in a drink that gives you a hangover, it is also related to certain chemicals that are fermentation by-products. That's why real drinkers know that some booze (whiskey for example) is a lot more likely to hang you over than others (like vodka).
It could be food poisoning, but not from a medium well steak. Cooked that much - it would have had to be green and smelly before cooking to be toxic afterward. But that doesn't rule out poisoning from some other food, or faulty food handling during cooking.
Actually, I think a little food poisoning now and then is good for the immune system. Let it add another bug to its reportoire.
