The first major issue is getting the
hot water thawed out and running again. Once it is thawed out, then it has to be protected from freezing again at all costs.
For the former problem, I like to heat water to near boiling temperature and use cups of water to thaw pipes. It really works fast, and yet prevents your house from burning down since there is no open flames. A hair
dryer also works, but is slower, and electricity is often hard to get at in some frozen pipe spots.
To prevent freeze ups again, adding insulation, spray foam, putting an electric space heater in the area, or opening up cabinets and doors all allow more heat to an area.
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The first issue you mentioned most likely is a loose fitting. Since you said "pressure switch" it tells me it is a rural setting, and since you mention it is clicking as water flows, I am betting you have a jet pump and not deep water pump. I have had this issue on a submersible pump to a lesser degree.
What happens is, as the pipes freeze, most likely at an elbow, tee or other joint, they expand by 11%, so the metal band clamps holding the fitting together, stretch. When the water is thawed, they stay that way and can loosen, allowing a bit of air to get into the system. For me, the water would drain back down my well so that every time the pump would shut off, it caused short-cycling. I think you will find, you have a loose clamp on the fitting where the water froze. You will probably be able to here a little whistle or air pulsing noise where the air leak is. I like to reheat the pipe and fitting with a hair dryer to get the black pipe and fitting softer, then tighten the clamp to get it nice and tight.