Teeth whitening is a cosmetic procedure that is not suitable for every patient (it is not recommended for sensitive teeth or for front teeth that have crowns or composite build-ups). You don’t have to whiten your teeth after orthodontic treatment, but if it is possible in your case, whitening adds extra brightness and charm to your smile. I recommend the procedure, and I have had it done on my own smile too.
This answer is for general information. Your own case needs an examination by an orthodontist.