You've got a few issues that may be affecting your blood sugars. Infection makes them go up (and vice versa). Lack of sleep and decreased exercise ditto. Wild hormone fluctuations probably don't help either.
Weight gain, brain fog, dry skin, fatigue - could all be thyroid. Your numbers don't look bad, but fertility docs like to keep the TSH closer to 1. Make sure you're getting your thyroid dose on an empty stomach, and not missing any doses.
Adrenal fatigue is controversial. Typically, weight loss would be the symtpom, rather than weight gain. Mainstream docs tend not to believe in "adrenal fatigue", but I think that's rather silly. There has to be some middle ground between perfectly normal adrenal function and complete adrenal failure (Addison's). Autoimmune adrenal disease (Addison's) is rare but somewhat more frequent in people with other autoimmune diseases. You might ask your doctor to check your morning cortisol level - not a perfect test, but would let you know if things are really off. (Note - too HIGH cortisol, Cushing's, can cause weight gain). I'd be careful about self-treating - cortisol like drugs will increase your blood sugars - but vitamin C and pantothenic acid (a B vitamin) can help support the adrenals.
Ask them to check you for celiac antibodies and vitamin B12 levels while you're at it. Both problems are more common in Type 1 diabetics. They'll say you can't have celiac because you're overweight but that's a myth.
Breast feeding is very important. I would shoot for at least a year. Breast feeding is not making you gain weight, I don't believe.
Are you eating differently in some way because you're breastfeeding? For instance, adding in lots of dairy products which you never used to eat before? (If you're suddenly eating more of foods you have some intolerance for, you might be bloating). Eating more prepared foods or restaurant foods with MSG (used to make obese lab rats in experiments)? Better for you and the baby if you eat a healthy, balanced diet of UNPROCESSED foods. Meat, veggies, whole grains, fish.
Exercise? I know that seems ridiculous right now, but you know it has a profound effect on your blood sugar status. If it's too cold to walk with the baby, time to do exercise videos or watch Denise Austen on the cable.
Don't forget to keep taking your prenatal vitamins too.
