If you rent and the electric is in your name you can definitely switch suppliers. But seeing as you rent if the landlord has other things pulling from your ‘unit’ that could be causing the high rate. I would call eversource and an electrician to have them investigate where that use is coming from.

Just wait until it actually gets cold and your heat has to do some real work to keep your place warm. So far this heating season has been incredibly mild. Consider your $600 bill a preview of coming attractions.