Hot water has more minerals and scale in it, especially if it sits in the hot water tank for long periods of time. Since you mentioned that you have a single lever faucet and your hot water works in the bathroom. My bet would be that your cartridge is clogged. I have this problem about every 2 years in my bathroom with a fancy grohe faucet. I have to take out the cartridge and clean it out, i have good luck with using and ultrasonic jewelry cleaner. Although, that is probably overkill. The cartridge usually has ceramic discs inside that regular pressure and mix the hot and cold water. You can try cleaning it or get the model number of the faucet and see if the hardware store caries a replacement cartridge.
One way to check if that is the problem is by taking off the hot water hose under the sink and sticking it in a bucket and then turning on your pump. If there is pressure at the hose then surely it is a problem with the faucet and since it is not the aerator, next thing down the line is the cartridge.