In dealing with some of my similar statements of frustration as a child, my mom would encourage me by affirming her love, as you have done, and also by assuring me (and showing me references, such as the examples below) of God's specific care and good plans for me. I do this for my DD7 and DS5 now, hoping that they will accept encouragement coming from an even higher authority than their parents. (: (I'm not trying to be overly "religious" in this post, just sharing what has helped in our family...)
Jeremiah 29:11
For I know the plans I have for you," declares the Lord, "plans to prosper you and not to harm you, plans to give you hope and a future.
Psalm 139:13-14 (King David's words to God)
For you created my inmost being; you knit me together in my mother's womb. I praise you because I am fearfully and wonderfully made; your works are wonderful, I know that full well.
