Perhaps someone knows a more technical grammar rule here, but adjective + pronoun combinations are rare in English. "Pretty me" is the slightly better choice of the two, but it's not very common or natural.
If I understand what you're trying to say, it would be more commonly said as:
"Even if you bring me gifts, you can't win me. I'm too pretty." or
"Even if you bring me gifts, you can't win this pretty girl." ("This pretty girl" still refers to "me"; it's the only way I can think of to say this naturally.)
A few special, set phrases have an adjective + pronoun in English. One is with the word "poor" (as in "unfortunate"):
"Oh no! Poor you!"
"I have a terrible cold. Poor me. :/"
But this pattern doesn't apply widely. It would NOT be common to say:
"Oh wow! Happy you!"