Transformer affect on Electric Bill
I have spent the last 22 years working as a engineer in the electric utility industry. I have seen complaints such as yours before. You said in your initial post that your KWH consumption has gone up. Here are some things I have seen in the past;
One time, a customer's air conditioner malfuntioned so that strip heat and the cooling were both running at the same time, working against each other. That made the consumption skyrocket.
Sometimes sediment will accumulate in the bottom of a water heater tank, causing the element to work harder. Also, both the top and bottom elements could be coming on at once. That would indicate a malfunctioning water heater thermostat.
It is unlikely, but it may be that your meter is malfunctioning. You might want to ask your utility to test it.
Some utilities, especially co-ops, have a demand charge for residences. So if you turn on several appliances at one time, the utility charges you for having the capacity in place to run all those things at once. If you run the dishwasher at one time and the clothes washer at another, you may save money.
Also, call your utility and see if they have a department that will send someone to your house and investigate your excessive consumption. Investor owned utilities many times will do that as a free service.
You said you had an eleven year door flapper living in your house. If your child plays outdoors a lot with the neighborhood kids, his coming and going will really let a lot of heat out and cold air in. Tell him to limit that, if possible.
Finally, I don't mean to alarm you but, there is an outside chance that your house wiring has a connection that has corroded and has therefore lost some of it's current carrying capacity. This situation can generate heat. Heat can lead to a FIRE. A licensed electrical contractor should help you with that.
Hope this helps,
George