For a first ever accident (didn't know there WAS such a thing!) it sounds like you were relatively speaking, very fortunate - fitting between those two "obstructions", thank Heaven! Did your airbag inflate?
But you MUST be traumatized from what you described. What a jerk, whether kid or DUI or nutcase - he put you very much in danger, and to a ton of trouble, whether or not you get reimbursed.
My last total (comes of driving older cars) was especially annoying because it was an "oldie but goodie" perfectly maintained CAMRY with under a hundred thou miles, and most infuriatingly, I too had just gotten four new tires. Of course, its intrinsic valuation and the new tires weren't factored into the car's worth. (I've since learned that it's not just Blue Book valuation but a portion thereof - at least with State Farm, 80% Blue Book).
That was the accident caused by an empty trashbin (trash day in an Ides of Mach wind!)
that somehow blew and wound up wrapped around my drivers side wheel. Caused me to lose control. Spun several times, ending up wedged against a tree off the road.
I ended up with several broken ribs, a severely undervalued car, and most infuriating, I was declared at fault! Even the car behind me hadn't seen the blowing trashbin. I call that an Act of G-d!
Jeez, I felt slight extrapolated trauma just reading about your accident - can't believe you escaped without serious injury (and yes, do check it out!*) So sorry you are going through this.
[*pique, that molar that fell off months after your accident, is almost incredible - especially that the auto insurance covered it ! Good thing that dentist identified its cause]