Kitchen Sink suddenly is only dispensing hot water!?

Our kitchen sink is suddenly not producing cold water. When I turn on the faucet, and turn the handle either direction, only hot hot water comes out. We live in New England and today we had a snow storm- don’t know if that makes a difference.This has never happened before. It seems only this sink, too. Any thoughts?
Another thing, one of the toilets was running for some time (cold water, too) so maybe that had something to do with it. Just hoping it’s not a bigger problem!
Thanks for your help!

How do you prevent plumbing clogs while saving energy and water?

I am trying to do my part to save water and energy by using cold water whenever I can for laundry, washing dishes and hands, etc. I also try to prevent wasting water by not letting the sink and bathtub run, and have installed a tankless water heater for near instant hot water. The problem is that my plumbing frequently backs up due to buildup of soap/shampoo/laundry detergent/dishwashing detergent. I’ve read that flushing the plumbing once a month with large volumes of hot water will help prevent/treat this problem, but that goes against my principles of trying to save energy and water. Does anyone have good ideas for preventing plumbing clogs from soap/detergent buildup, without wasting a lot of energy or water?