Translation:I am almost another person with him.
She is a girl, she likes a guy. When she meets him, she gets all crazy nervous and stuff, loses her mind, becomes like an another person.
The guy takes her to the restaurant. Girl can not handle her emotions anymore because of how much she likes him and the effort she puts in to impress him with her silly jokes or some silly stories that she usually never tells to anyone, it is all over the top, she has to talk with someone about it, ask for advice or somethin, so she excuses the table, goes to "fix her hair" to the rest room and calls her friend and says ( Jeg er næsten en anden person sammen med ham, hvad fanden skal jeg gøre?).
Seems like some people are confused about this phrase, so this is my version of when it might be used? Proceed with the story with your imagination if needed. :)