Actually, most of us say "shoulda, coulda, woulda, etc." Have is the only word that goes with those modals in the past perfect tense.
If you are an English speaker studying English. the first thing you should realize is that speaking English and writing English are two completely different things. Something that can be very clear when spoken can be confusing when written, and vice-versa.
Now for my teacherly advice: Pay attention in class and practice, practice, practice. You may not become a good writer, but you will get to Carnagie Hall.