Considering braces. Unhappy with "~" shaped smile. Back teeth feel like they touch on one side. Recent dental xray in profile. Recommendations?

start with gp. Solving a smile problem is often multi faceted. A general dentist will help you understand if orthodontics will be part of a solution appropriate for you. Sometimes a combination of orthodontics, surgery, and restorative dentistry is needed to fully solve complex issues. It's best to have a good quarterback who can refer you to appropriate specialty care as needed.
Team approach. If your "bite" is off, you need an orthodontist. If teeth have worn unevenly or are discolored, you need a restorative dentist. If gums unhealthy, you need a periodontist. If jaws malposed, you need an oral surgeon. Start w general (restorative) dentist who will help you develop your individualized rx plan based on your needs, and will refer you to appropriate specialists if indicated.