So, are you saying that you've had braces but they haven't left you with the perfect smile? I think in that case its a cosmetic treatment and your dentist is right that it is isn't covered.
tbh I don't know what else you can do. You could plead with the orthodontist that its not corrected yet and could he/she have another look - but it does sound like its a cosmetic treatment and so would need to be done privately which will cost a serious amount of money.
Sorry

Jon