Drinks high in sugar and acid can corrode the metal parts of braces, making them rougher, which can hinder tooth movement and slow down treatment. In addition, the sugars in these drinks stick to the teeth and braces and are turned into acids that weaken the enamel and can lead to white spots – the first stage of tooth decay. To reduce the risk, it is advisable to limit how much of these drinks you have. If you do have them, it is best to rinse your mouth with water straight afterwards or to have a dairy product such as milk, ayran (a yoghurt drink) or cheese, which helps to neutralise the acids. Brushing your teeth immediately after acidic drinks is not recommended, because the enamel is temporarily weakened. It is best to wait around 40 minutes before brushing, to avoid further wear to the enamel.
This answer is for general information. Your own case needs an examination by an orthodontist.