Milk is considered a whole food so fills them up and they don't want anything else. But if she is tired/pale I would be getting a second opinion. Does your multivitamin have iron? I would think about getting an iron supplement like ferro grad to encourage her appetite. Try small pieces of fruit raspberries were a hit when we went through similar food issues. Also is she constipated? Dd had issues and didn't eat much at all until we started to sort that out.