Water pump wont shut off

The waterpump in my daughters pulltype camper wont shut down. It seems to build pressure then quites down and there is pressure at all lines but the kitchen sink cold water is just a trickle. Traced all the lines and there isn't a leak. Should say it shuts down a bit when the pressure is built up but never shuts off. I could see where it might have a kink in the line or something blocking it as a reason why it is just a trickle but cant figure out why the pump will not shut off. Ive went over every inch of that cold water line and no leaks. Maybe the pump is bad or any other reasons for it? All other lines seem to have plenty of water pressure so thinking something got in the water line to the sink but shouldn't the pump shut down anyway? Any ideas? Thanks, JIm