Could it be "Nihal from the Land of the Wind"? She is half-elf, can't really use magic so she becomes a dragonrider, her dragon OARF lost his previous rider into battle and doesn't like Nihal at first.   
http://www.liciatroisi.it/books/nihal-eng/  
I found a detailed summary but only in italian, should be easy to automatically translate it: https://it.wikipedia.org/wiki/Nihal