does my car have rear shock absorbers

Yes, Every passenger vehicle in North America has rear shocks. I'm sure there are caveats to that, but the 300 certainly does have them. If your shocks are leaking any fluid, damaged, or the vehicle feels bouncy or hard to control, especially over bumps, then shocks may be needed. If you would like a certified shop to diagnose your issue, see here: http://repairpal.com/chrysler-within-10-miles-of-washington-district-of-columbia-20002