In your case I think you have a variant of Pruritus ( a sensation that elicits a desire to scratch) with Urticaria features.
Diabetes is a systemic disease and one of the causes of
Pruritus.
Look also into low thyroid function and specifically Myxedema, a dermatological feature of hypothyroidism.
You seem to fit the profile, because high cholesterol (a) and
intolerance to heat/cold changes (b) are common in hypothyroidism.
Add to this the higher prevalence of hypothyroidism (c) in
diabetes-up to 30% in diabetic females- and the 3-fold increased risk of high blood pressure in people with hypothyroidism (d) and now there are too many possible factors to be considered coincidental.
I would strongly suggest you get Free T3, Free T4 and Reverse T3 thyroid tests done.
Please forgo the standard tests which can miss the majority of cases of hypothyroidism, since they measure only serum levels and totally ignore thyroid resistance (type 2 hypothyroidism).
Some self-care tips:
Bathe less frequently, use cooler water, spend less time in the bath, use natural fabrics which breathe well and are skin friendly like organic cotton and silk, avoid spicy foods, avoid caffeine and alcohol, apply an organic aromatherapy cream
with peppermint oil.
Please list your meds including strength and dosing,
and I can check them for you.
Best wishes,
Niko