"Sut dych chi? Wedi blino!"
Translation:How are you? Tired!
That's right, wedi blino just means "tired".
"I'm tired" would be Dw i wedi blino.
blino is to tire; wedi can mean "after" and is used to form the perfect aspect (as in "I have done" from "to do"), so a more literal translation would be "after tiring" or "have tired".
But it's probably best to simply treat wedi blino as a fixed expression meaning "tired", because that's how we would express it in English -- we say "I am tired" and not "I have tired out".
Note also that since there is a wedi, it doesn't need yn -- "I am happy" would be Dw i'n hapus but "I am tired" is Dw i wedi blino, not *Dw i'n wedi blino with 'n.