Rheem Hvac system total electric RHQA1620J Just bought house no nothing about heat pump. Electric bill for the first month I lived here-$nearly $ 600.00 for a modest house and a single working person. I noticed the outside unit making a very loud whining noise and the fan blades were not turning. Today I hit the reset button and the fan blades started to turn but did not come on-making a very faint humming noise. Help I do not know what to do I have to have heat

It could just be the fan capacitor in the outside unit or the fan motor itself. Usually it is cheaper to just replace the capacitor first and if that does not work then replace the motor with the appropriate capacitor for the new motor. If you had a capacitor tester it would make the job easier but as a home owner you probably do not have that tool.

No matter what you do you will need some skills in electrical work and electric wiring so be prepared for that issue or call for on site service.

Your electric strip heaters should still be working so you have heat but they will cost a bit more to operate than a heat pump.

Thank you, also I have noticed that the inside unit keeps running even when the light is off. My electric bill was way too high last month. I am keeping at 70 after reading everything today but now I am also concerned with the inside unit running constantly. I know it has cut off but not often. Can I just turn the whole unit off when its through running and then cut it on

Yes you can but then you will get temperature swings. You should get the outside unit fixed.