The motivation to start orthodontic treatment can come from different places – the patient's own decision, advice from a relative or a referral from a general dentist.
Whatever the reason, before starting orthodontic treatment it is important for the teeth to be prepared – this includes a preventive check-up with your general dentist, treatment of any decay (if there is any) and removal of tartar where needed.
There is no wrong order – you can see an orthodontist first, who will refer you to a dentist if needed, or the other way round and start with a routine dental check-up.
This answer is for general information. Your own case needs an examination by an orthodontist.