Remember that everyone's face has some assymetry. Ofcourse you will notice your assymetry more then anyone else. I would make an appointment with your orthodontist and express your concerns. There are different type of retainers (example - spring aligners, hawley retainers - fixed (permanent) retainers), but only your orthodontist who can examine you clinically can determine which would be the best in your case. Good luck!
I would recommend visiting your orthodontist to address your concerns. As orthodontists, our mission is to always ensure that our patients receive beautiful, healthy and functional smiles. There several different retainers to choose from but your orthodontist will know best which one to use once he/she visits with you. In regards to another set of braces, that is hard to judge based on your pictures. You have a beautiful smile and your orthodontist will guide you in the right direction. If concerned get a 2nd opinion!