You pretty well know something let go or really got damaged. I would get it up on a suspension hoist and have a hard look around. If not obvious use a pry bar to check that something is not snapped off or destroyed. Since you are experiencing rear steer I would do it right away. Hopefully it is not too bad. There is a possibility that whatever is causing the new rear steer could totally let go at any time. As for insurance covering it. Some places allow road claims against the state or province but do not hold your breath. If you had collision or comprehensive on your car you might get it covered as well. Also there might not be much really wrong and not very expensive to repair. If I remember right when you ran over the deer it is a comprehensive claim with no deductable. How did you miss seeing the deer you ran over anyways? Or was it just unavoidable? The nice way insurance companys treat people in general have made them open season to some of us extremely satisfied claim filers. They have become far too creative in trying to lay it back on their customers. Poetic justice?