It's the second one: I'm multilingual
"Multilingual" is an adjective, so it can be used to decribe "I", but if you add "a" in, then it begs the question "You're a multilingual what?"
Consider another example:
"I am big"
"I am a big" (A big what? What noun does "a" refer to?)
Cheers
John.
On the other hand, if i wanted to add a noun in the end, would it be right to say: I am a carnivore girl.
Sometimes in casual English the noun may be left out if it's obvious from the context. For instance, if we work in a shop and I say to you, "That guy is a regular." In that case regular=regular customer.
Occasionally the association of adjective-noun becomes so strong that the adjective starts to take on the feeling of a noun - as in the case of "regular".
However, if you're learning English it's best to stay away from that sort of idiom, because only experience will tell you when you can safely leave the noun out.
Re. Carnivore: This is a noun, so it should have the article "a" before it.
On the other hand, if you say, "I am a carnivore girl", that is a very casual, informal way of speaking, to use a noun as an adjective. The proper form would be: "I am a carnivorous girl."
Cheers
John.