I have been in this boat!! I weighed 110 lbs (at 5'9") and it took all of my energy just to keep the baby, the toddler and myself clean and fed. To make a very long story very short: I saw an endocrinologist, was diagnosed with hypothyroid and "an adrenal episode."
It was a whole host of things coming together that finally helped, but my initial recommendation is a thyroid test and a cortisol test (may have to seek out a naturopath or chiro for this). Search "adrenal fatigue" in the forum for some great info on some very good and natrual ways to get past the burn-out.