I have a deep drilled well with supply lines split to feed the house and livestock watering respectively. The flow to the livestock line remains constant regardless of water usage in the house. But with everything turned off in the house except one faucet, when a toilet is flushed the flow from the faucet reduces to a trickle. Pressure at the well remains at 45 to 50 lbs. What's up? Also, whenever lightning strikes nearby, I get mud in house water. I'm perplexed.
My guess is there is a restriction in the line going to the house, with only enough getting through to feed one thing, either the toilet or the faucet. And since the toilet is probably drawing the water first before the faucet, it goes there.
I agree that it is more likely just heavy rain that is causing mud in your water. However, surface water getting into your water supply is bad news. You should consider adding filters to clean up the water supplied to the house. I'd guess a chlorine injector to kill any bacteria in the water, a tank to give the chlorine some time to do its job and let mud settle out, coupled with a filter that can take the remaining mud and chlorine out.