Example: 1.Today I have a hang over because last night I drank too much wine. 2. Last week I was hung over as well because I drank too much champagne.

To be hung over = to have a hangover because, although 'hangover' is one word, it comes from two words, hang+over. the verb is hang. past tense is hung.

There is no such word as "hougover". A hangover is what you have the morning after you have been drinking a lot the previous night.