Sorry to hear of your issue, I agree with the great advice from everyone here.
Oil is not friendly to rubber, plastic, & paint. Since your engine caught fire I would also have it towed to the dealership and have them inspect it. If something is wrong you don't want to find out while you are driving - especially if it's safety related. Get the quickie lube to pay for the tow/inspection/repair. They should also be paying for your time, but good luck getting that back.
If they hedge, tell them they should be happy they're not having to buy you a new car.