Can I sue the auto repair shop for the damages to my car

I took my 2012 Mazda 3 into Mazda for an oil change . They forgot to put oil back into my car and the car stopped while I was driving on 12/24/17 . They gave me a rental replaced the engine and now there are issues with the engine they are wanting me to pay over 1000.00 for the repairs . They told me the engine was under warranty but not the parts to the engine . Prior to their mistake I kept up with my oil changes had inspections done on my car to make sure everything was ok only doing business with Mazda . I was in college when my mom got the car for me brand new from Mazda I traveled from Memphis to Nashville so my mom made a point to keep up the service on my car .