"You are my only friend" is the obvious good translation, but I also question the grammatical correctness of "You are the only friend of mine".
Frankly, I am not sure whether "mine" should be used in this way or not and welcome any comment.
I know that people often say things such as "She is a friend of mine", but "mine" is a possessive pronoun and I think its proper use is in sentences such as "This is mine". That is, I really think that it means "that which belongs to me". Thus, I wonder if it is grammatically correct to precede "mine" with "of". Perhasp someone can explain whether it is grammatically correct or not.