Sounds like you have a lot going on barrettscv. Have you been riding all winter or within the last month or two? Without a picture its hard to get an idea a) what shape you are in? and b) your riding posture in both drops and hoods.
Usually typical muscle pain lasts for only a couple of days (DOMS), but with the lower back can last longer. Rest is usually the soundest advice along with light stretching at first working your way up to longer holds. Ice and compression can also be used depending on the severity along with things like tylenol or alleve (but don't use to long). Also core work and total body work may help. If you've been going hard you also might have CNS overload and need anywhere from a week to a month off, but that is usually built into periodization training.
My advice would be to rest and stretch. Also notice any little things like a slight lean or tilt to one side as this might be indicative of a muscle imbalance. Keeping your wallet or something in your back pocket and constantly sitting on it. See if your mattress is sagging or dipping and see if you can prop it back up.