To answer your question simply, if they were previously connected to O and W/X2, there is no risk of damage if they are reversed but you will experience the symptoms you have if they are indeed reversed from the way they should be. If the other wire were connected to their corresponding terminals on a Trane heat pump thermostat, this is how you should wire your new one:
*Red to R (leave jumper to Rc)
*Blue to C (if your new Honeywell has a C terminal, otherwise tape it up and tuck it back in the wall)
*Yellow to Y
*Green to G
*One White to W/Aux/E (if Aux and E are separate terminals on your new Honeywell thermostat (some Honeywell's are like that) then you should install a small jumper wire between Aux and E.
*Second White to O/B
Since you don't remember which white went to which terminal, you just have to try it and see if the system works right. HOWEVER, there's a step you have to complete in the thermostat's installer setup program as stated in your manual first. You MUST tell the thermostat what type of heating/cooling system you have. So you would enter installer setup and under type of system, you should select "Heat Pump With Auxiliary Electric Heat" (or just HP with Aux heat). Depending on what model thermostat you bought, there may be another setting for what type of backup auxiliary heat you have so scroll through the instructions and if so, choose electric heat for the type of backup or auxiliary heat.
Then and only then can you make sure the two white wires are hooked up right or wrong. If wrong, it will heat in cool and cool in heat. Just switch them and you should be fine!
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