Brief Answer:
Hormone tests

Detailed Answer:
Sorry to learn about your bothersome symptoms.

Some possible causes of sweating are:

1 An overactive Thyroid condition called Hyperthyroidism

A simple blood test called TSH can help screen for this. I see you are on thyroid medicine. If the dose is excessive for you, then it is equivalent to a 'hyperthyroid' state

2 Acromegaly

This is an uncommon disorder but can be tested for by doing a blood test called IGF1 (Insulin like Growth Factor) 1

3 Pheochromocytoma

This is another rare condition in which affected individuals get spells of sweating associated with chest pain, shortness of breath and headache.

A blood test called Plasma Free Metanephrines can be useful in detecting this.

4 Menopause-related hot flashes

If your menstrual cycles are regular, then this is not the case with you.
When I see someone like you in my practice, I typically order the following blood tests in addition to a detailed physical examination:

CBC (Complete Blood Count, also known as Hemogram; includes Hemoglobin, WBC and Platelet counts)
Electrolytes (Sodium and Potassium in particular)
HbA1c (Glycosylated Hemoglobin = your last 3 months' glucose average). Also known by other names such as GlycoHemoglobin or Glycated Hemoglobin or A1c
Liver function tests (SGOT , SGPT, Albumin, Bilirubin, Alkaline Phosphatase)
Kidney function tests (BUN, Creatinine)
TSH (checks your thyroid)
Free T4 (this too checks your thyroid) Thyroid autoantibodies : Anti Thyroid Peroxidase (TPO) antibodies and Anti Thyroglobulin antibodies
25 hydroxy Vitamin D levels (ideal range 40 to 60 ng/ml = 100 to 150 nmol/liter)
Plasma Free Metanephrines
IGF1

None of these tests require any fasting and can be done at any time of the day

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