Get a dogbone adapter
(click here) like this and use RoyB's polarity tester. This will work just to be sure where every you're plugged into is wired correct.
A surge protector will provide much more insurance, not just for high voltage or high voltage spikes, but also low voltage, which can reek havoc on your air conditioner! The surge protector (made for RV's) will kill the power before a spike, high, or low amps can cause any damage. The price of a replacement air-conditioner will cost a lot more than an RV surge protector, not to mention the down-time you won't be able to use your camper while, whatever got damaged, gets fixed.
I have one of these: