No doubt you have a problem. Believe it or not it could be as simple as one thing running in your home that is drawing quite a bit of electric. Seeing as how you mentioned the new HVAC, it could very well be a new thermostat could fix the problem (programmable preferably). I would also assume the coil was replaced with the HVAC, suggested but not always necessary. While most AC companies will tell you it is practically mandatory to replace the condenser as well, but seeing as you are posting this in this time of the season, I donâ€™t see this being the issue.
I had the same issue not too long ago where my electric bill was through the roof for 2 months straight without logic.
I finally decided I had enough. Here's what I did: First I changed to a programmable thermostat. Donâ€™t have temperatures differentials range more than 4-6 degrees in any given period over a constant amount of days in your cycle as this indeed costs more than just leaving the unit running at an acceptable comfort level or have the programmable start lowering/raising a degree gradually over the day. This will help save quite a bit of money as opposed to coming home and dropping the thermostat 8 degrees since it will take longer for the area to cool, hence making the unit essentially run longer and work harder to reach ideal temperature all at once.
Next was trial & error. I looked at the spinning disc dial on my outside meter and it was spinning about 3 revolutions faster as compared to the 1 revolution of my neighbors meter who I always joke is a stock holder with the electric companies. I went and flipped every breaker in the house off, turned on every light in the house, called a friend who flipped 1 breaker at a time and systematically go and disconnect or turn off anything that was drawing power off the circuit while I watched just how much each item was pulling as proof by that wonderful spinning disc to see just EXACTLY what was being such an electric hog.
30 minutes later (and a very confused friend on my hands who assumed I was neurotic) and we found that the lava lamp on my desk in my office that I had acquired about 2 months earlier which ran 24/7, the laptop in my office which ran 24/7 and another monitor I had in another bedroom that wasnâ€™t shutting down (which I didnâ€™t realize until that day) when disconnected made a surprisingly huge difference in my electric bill.
Thinking more about the new HVAC you said was installed, this may in fact be a culprit or just a well-timed coincidence. There may be a leak somewhere. The only way to know for sure is to see if itâ€™s running constantly (meaning it's not heating or cooling as needed because of the misdirection or escape of cold or hot air somewhere else). If all else fails, you may want to call your utility provider and simply ask for help. They are usually pretty good about referring low cost or sometimes free services that will help you make your home more energy efficient.
I hope this helps, for the sake of your checkbook!