Two weeks ago on a nice sunny 80 degree day, I decided to wash down the coils on my heat pumps. At the time, one was running and one wasn't. I tried to be careful not to spray water near the fan or electronics. To make a long story short(er), the heat pump that wasn't operating blew the breaker repeatedly afterwards. This went on for a few days (I kept trying and the weather was cooperating). After nearly a week, the unit stopped blowing the breaker and seemed to be operating fine. The unit is able to control temperature in both AC and Heat modes. The problem is that it seems to be constantly operating and every minute or so it makes a buzzing sound, the unit shakes a bit, and the lights flicker in the house. Last night I disconnected the contactor and cleaned the contacts, but it didn't help. Any help?

Check the run capacitor, check amperage to fan and compressor, call a pro.

Have your service technician install a Kick Start capacitor device. They cost about $30.00 and it has two wires that connect to the compressor run capacitor. Sometimes compressors need a little boost in starting for several reasons including voltage drop when trying to start up.