The best way to correct your asymmetry and bite is with orthodontics and jaw surgery. The severe crowding of the upper arch will require extraction of a pair of premolars. You may or may not need extractions in your lower arch. As far as surgery goes, you will need an asymmetric mandibular set...
Most likely it is OK, however, your Orthodontist knows your treatment plan best, so I would recommend that you call to let the office know what happened. If they need to see you sooner, they will let you know.
If you are missing a tooth and are going into braces, a tooth can be placed on the wire and brackets while you are straightening your teeth. We always try to make the patients feel comfortable while they are transitioning!