Didn't you buy any type of road hazard warranty? Since the tires are brand new they should have some type of warranty. Even though this is your fault, it still falls under this type of damage and protection for you. I get my tires from Discount tires with the road hazard warranty and this happened to me too. I brought it in and it was covered under that warranty and they replaced it for free! I did pay $15.00 for a new warranty for the new tire that was put on.
