1. Was the car insured?
If your insurer has agreed to pay, then collect the money, and move on.
You may need to use any insurance money to pay out any loan you have in respect of the car.
2. There will almost certainly be some sort of "all care but no responsibility" arrangement
between the tyre place and the customer. The tyre place will probably try and tell you that
that releases them from all liability in respect of this accident.
That's not always and automatically correct, but I don't know enough about the facts and circumstances
to give you a more useful answer than that.
3. You may have an action against the tyre place regardless.
That said, this is probably not a DIY matter. I suggest that you'll need a lawyer to assist you.
Ask your lawyer to advise you on the prospects of success of an action against the tyre place.