I think it's very normal - one thing which might help would be to think about how this person
isn't like you - you're chatty, she's taciturn, you're hyperbolic, she's downbeat, differences of age, background, nationality, you're feeling gloomy today, she's serene... and focus on how that might affect her voice as a narrator.
It can help, too, to think first about how she speaks aloud - sit her down with a friend and a bottle of wine - and then work out how that translates into her narrative voice.
The other thing you could do is to take a passage from a third-person narrative which you feel is quite strongly
not you - where the close PoV of the character colours the voice of the narrative quite strongly - and mechanically switch it into first, just changing pronouns and verb-forms, as it were; essentially, making that character also be the narrator. Not to create a great work of literature but to explore the way that close 3rd is really very like 1st...
I don't know if you know my series on PoV and Narrators, but it might help you to think through the issues:
http://emmadarwin.typepad.com/thisitchofwriting/2011/10/point-of-view-narrators-1-the-basics.html