It sounds like dirt has gotten into your water lines, and is now preventing the taps from closing fully. Remove all faucet aerators and run the water at full blast for 15 minutes.

If you are working off a cistern system your water pressure is too low. You need to let it build up again before you are back to full pressure.

My family lives in a rather isolated farm town in the countryside. My brothers were washing the car and left the hose on. Now the water indoors won't turn off or is a very slight flow of water. What is wrong, and will it return to normal soon?