For some reason, I get very little cold water to my master bedroom shower and sink. The problem is isolated to this bathroom only. The rest of the 3 bathrooms are fine including the other second floor bath. The water is almost scolding hot. When I turn the shower knob to cold, I get very little pressure and it barely cools down. If I turn the both sink knobs to cold (it is a two sink bathroom), the pressure is fine but stays scalding hot for over a minute before it gets cools down. If it was isolated to the shower only, I would replace the cartridge in the fixture but it obviously isn't. Could it be a blockage in the pipes leading to this bathroom only? The house is 15 years old. Please help! Thanks in advance.

Is the water heater located next to the bathroom with the problem? Water heaters can stratify with hot water backing up into the cold lines. Over a minute seems like a long time for the cold to finally get to the faucet.

Does the shower valve have integral stops? If so, close them and see if the problem in the sinks goes away.

Your shower cartridge may be causing a cross connection from the hot to the cold, and have a balancing spool stuck. Shut off your water at the main in the house, then shut off the cold water inlet to the hot water tank. Disassemble the shower valve and remove the cartridge and any loose pieces. Have someone turn on the water to the house again for 2 or 3 seconds and see what kind of cold water flow is coming from your shower valve. If you have good flow, replace the cartridge; if you don't, I would go hunting for a partially closed shutoff valve. If you have a hot water recirculation system, you may have additional problems, but I would definitely start with the shower valve.