The air bladder in that blue pressure tank may be leaking. If it is, you will have to replace it.
Check it with the air valve on top. If water blows out of that air valve, the bladder is definitely shot.
If water does NOT shoot out of the air valve -- with the power to the pump OFF and the water pressure drained down -- check the air pressure with a tire gauge. It should be two PSI below your pump cut-on pressure (e.g. if the pump is set at 30-50 cut-on/cut-off, it should be 28 psi).
If it needs air, air it up with a bicycle pump or portable air tank or compressor.
The storm may have flooded the top of your well head, and it may just clear itself up.
If you keep having problems, you need to call a well-and-pump man or a plumber experienced at working on them.