When you store the shore power cord, do you plug the end into an outlet that connects it to the generator? If not, the changeover is performed by an Automatic Transfer Switch, a relay that switches to generator when it's available and passes shore power through to the breaker panel when the generator isn't producing voltage.
I did not know about this, I need to check this out
Did you turn off all of the major loads (air conditioner, etc) before shutting down the generator? RV transfer switches lack the logic that commercial transfer switches use to ensure that the generator and shore power are in sync before switching. If you had anything running, there's a good chance that the transfer produced a large current surge that damaged the transfer relay.
The frig and some lights
Check the circuit breakers in the power panel, in case the surge tripped one or more of them. Sometimes a breaker will trip without noticably moving the handle, so turn each breaker all the way off and then on to reset it.
The transfer switch is likely in a metal box on the rear of your power center. To find it, trace the wires from the generator or shore power and the first thing they enter will be the transfer switch.
There's not much that's user serviceable, other than making sure all of the connections are tight. If you do start poking around, make sure you're unplugged from shore power and the generator stays off.
