"You are dear to me" is pretty common. If she's American, it sounds like she's not ready to commit. She wants you to know that you are important to her, but she probably needs more time before she feels comfortable telling you she loves you. This is my best guess based on what little youv'e told us.

it means that...  you're head over heels in love with her

Ou. Maybe the correct variant - "You are dear TO me"

I have never heard, "You are dear for me".

Maybe she means, "You are in love with me" ?