I am headed home on Sat night doing about 80 on my Accord Coupe.
Little Bambi decides to jump out in front of me. I veer right and the
car starts fishtailing. I tried controlling it but ended up doing a
complete 270 with car pointed the wrong way and smoke everywhere.

Someone was looking out for me because traffic was at least a mile
away. I immediately straightened the car and drove off. When I got
home 10min later it was still smelling of burnt rubber.

Question:

Car seems to be driving fine but should I be checking it out for
anything?

What possible damage could I have done?