I think you should go back to the clinic and ask them to help you understand why they feel your daughter's problem is not ADHD, but rather an emotional problem. If you are not satisfied, or confused by their answer, then you certainly should get a second opinion. I would suggest talking to a psychopharmacologist (a psychiatrist who specializes in the diagnosis and chemical treatment of emotional problems). Make sure you consult someone who has lots of experience with kids who have ADHD. Your daughter's pediatrician should be able to make a referral.
You should be aware that when teenagers are depressed, they commonly have difficulty focusing on schoolwork. When kids feel better emotionally, they can think more clearly and pay attention more easily. Depression in most children (and adults) can be effectively treated with a combination of therapy and medication, which the clinic may have recommended. This may have been hard news to hear, especially when you went in asking about ADHD. However, a treatment team is doing a good job when they consider all of the possible reasons for an attention problem. If you take your child to someone who only specializes in ADHD (e.g., a special educator), he or she may lack the expertise to diagnose depression.