"No...we did not realize the extent of the damage of the plane until we saw the outside and reviewed our own photos of the exterior, but we did know that something went very wrong. I also know that I was in tears, in fear for 2 days before getting back on the plane"
I highly doubt that you got back on the same plane, apparently has been announced that the aircraft must be repaired in place (no surprise) and in fact will probably be written off due to repair costs.
I do agree with I need a name though, if you have the injuries you describe, you should have seen a doctor upon your arrival in the Dominican Republic, which I am sure would have been covered by Skyservice due to the nature of the injury.