I honestly don't know what's going on, and neither does my pop. He held the pressure switch handle and it shot back to over 40lbs. We measured the pressure of the tank and it was around 18lbs. Everything seems to be running normal.
Sounds like the pump may be working.
Something similar has happened twice now in the past month. Both times it's happened, it was right after the toilet didn't stop running. No telling how long the toilet had been running the first time. We thought the well dried up, since we had no water. A few hours later and a replaced pressure switch and we had water again. We recently had over 3 inches of rain too and everything has been fine.
The well running out of water is a possibility, of course. And the water level coming back up with time would be common. Is running out of water in wells near you common-- are you in California? If there is worry that your well might run out of water, you should add a protective device to shut the well down in that case.
http://cpkits.com/collections/cycle-sensor-pump-monitors is a such a device sold by Valveman's company. The device gets wired between the breaker and the pressure switch. It can be located by the breaker box or at the pressure switch.
Your pressure switch with the low-pressure shutoff offers some of that protection, and it may have saved your pump. However it will not shut the pump down if the water pressure rises higher than the cut-on pressure, but there is not enough water to hit the cut-off pressure, and you are not using water.
I asked how far down the water is. No clue? You might reflect the sun down the well, and try to estimate the distance. You could drop an ice cube to maybe help see/hear what is happening. You could lower a strong cord or extra-strong fishing line with a non-lead weight/bobber to measure water depth. If the water was not much higher than the pump, it would be more likely that you would run out of water.
Could a toilet running nonstop cause this? Some sort of flooding or something?
If you pull 2 GPM continuously from a well that produces 1.6 GPM of water, could it run the well dry? Yes. This may not be your case, but it could be for all we know.
Rain would not usually soon affect the water availability in a 300 ft well, but it could happen in some cases.