I had the exact same situation during Uri in 2021 following 36 hours of no power and dripping faucets, Houston area. Unfortunately I’d only been dripping cold water faucets due to bad advice and not yet understanding the mechanics of the plumbing system. Once I discovered the freeze I opened the faucet fully and once power was restored I set a space heater pointed to the pipes underneath the sink and eventually it started flowing again. No damage but we have pex which are supposed to be more resilient to freezing incidents. Since then I’ve dripped both sides and always treated that area with care in freezes since as that proved that was the weakest link.

Where is your shutoff valve in case your pipe froze and split?

Turn on the hot water to that faucet.

Feel the pipe under the sink. Is it frozen?

Pipes are typically in the wall, attic, or under the home. Try to get heat to the pipe by opening the cupboard doors to expose that wall to the heat.

Turn your home thermostat up a few degrees.

Hard to say without seeing your setup (and my first coffee hasn't hit my bloodstream yet) but ya, it's probably a frozen spot in the line between your hot water tank and the tap that isn't working.

It happens to me once or twice every year... I live in Canada in a very old house where the weather has been into the -30c (-22f) lately. Open the tap, and You'll need to pour some heat on that part of the line where it's frozen to help it thaw using either a heatgun/ hair dryer or torch. (Careful if you're using a torch or heatgun to not put too much heat on the plumbing joints where they're soldered... assuming you have copper lines.) Tapping on the line while putting heat on it helps a bit to break up the ice, but be careful not to hit it too hard.

If it's in a crawlspace you might be able to stuff a space heater in there and let it warm things up too.