There is a good probability that there is some trash (a bit of sand, plastic, etc) hung up in the backflow preventer that is associated with the pump. With the city water turned off, turn on the pump for a few minutes, with a faucet open, so that the trash might be pumped through.
If this does not fix the issue, you might have to repair it.
If flushing does not remove the trash quickly and return operation to normal immediately, you can continue to camp anyway. Fill the water tank as needed and use the water from the tank. Over a few days this may fix the backflow problem.
2014 Silverado LTZ 1500 Crew Cab 5.3L maximum trailering package