1. You are a girl aged between 13 and 19 years old.

(Which one is missing between 'girl' and 'aged'? is #1 from #2?)

2. You are a girl who is aged between 13 and 19 years old.

Both sound really wrong. We'd never say either.

You are a girl between the ages of 13 and 19. (The "years old" is redundant, but can still be put in there.)

In sentence #1, the missing word is "who". The correct version of the sentence would be "You are a girl who is aged between 13 and 19 years old." Sentence #2 is the correct version, where all the necessary words are included to express the intended meaning.