You didn't say but I assume that your trailer is wired for the standard 30-Amp service.
First, check your neutral wires to a good ground. This should never show any voltage reading.
Assuming that your trailer's power system has worked normally in the past, I would check the following;
1- Is the external RV power cord that is plugged into the campsite power box OK? Is there any damage to the cord or any oxidation on the contacts?
2- If the cord is OK then I would contact the campground and have them check out their campsite power box wiring.