I drained my hot water tank one week ago. Since then, I've had to replace my whole home filter twice due to the filter being clogged. We have well water. I have also noticed the hot water coming out of sinks, etc. sounds like it has air in it.
Are you getting hot water out of the cold side?
If you are look at the pressure gauge and see what the pressure is. Depending on the pressure switch you have..most common 30-50 of 40-60 switch you should have a reading of either 40 or 50 psi. Most wells are set up with the 30-50. Where the pump turn on at 30psi "Cut in" and turns off at 50psi "Cut out"
If you get hot/warm water out of the cold you could have the stages in the well pump out where the system is not building up pressure like it should. Making the pump run and warming the water around the pump and being pumped out when you turn on the water but noticing it on the cold side more than the hot side.
Have you noticed a higher electric bill?
I'm just taking a stab at this because I don't fully understand your post " I have also noticed the hot water coming out of sinks, etc. sounds like it has air in it."