People also say "I'm fucked up" when they're really drunk and might do something stupid. "I am fucked" means things are really really bad for you. "I sent the e-mail to the entire company by accident. When the boss sees it I'm fucked."
I fucked up means that you messed up ... you did something you should not have
I am fucked up ... that's more like there's something wrong with you as a person psychologically ... so it's not really something a person would typically say about themselves unless they had an epiphany about how messed up they are as a person.