May I file a claim against an auto repair shop?

You have a case if you can get proof (probably in the form of an expert opinion) that the fire was caused by some negligent act by the repair shop.  I assume that your insurance covered  your loss except for your deductible (which means that your insurance company will likely assert a claim against the repair shop for the money it paid out - this is likely to be worked out between the two insurance companies, yours and the repair shop's, with no litigation).  The total amount that you can recover would be the deductible plus the amount you paid for repairs, plus some incidentals (e.g. cost of rental car for a while if you needed one.)  Not sure if this will be worth it to you, since, even if you can get an attorney to handle the matter on a contingency, or you decide to represent yourself, you will probably need to pay an expert.