I have cold water coming from my bathrooms,utility tub and showers,but none from my kitchen cink,my faucet is one handle.What should I check for ?

Start by closing shut off valves below sink. Then remove the cardridge, and open the cold valve, do you get water then? If not, remove the supply line off the top of the cold water shut off valve(with valve closed). Then slowly turn on valve and see if you get water there. Try these two things and let us know.