What could cause the water flow in house pipes to suddenly be altered?
Yes, it does sound like a pressure tank problem. Without a properly functioning pressure tank, the well pump has to try and maintain pressure with fluid alone. That's what you're seeing at the faucet--the cycling of the well pump as pressure very quickly jumps and drops. 

The problem could be a tired bladder or a leaky seal elsewhere. Try re-pressurizing the tank according to the manufacturer and see if it holds, and check for leaks at the fittings.