Could Severe Sweating, Trembling In Hands And Mood Swings Be Due To Thyroid Disease?

I am a male, nearly 30 yrs old. I sweat profusely with little activity, my hands tremble, often have bowel problems especially diarrhea, borderline high blood pressure. Suffer depression, anxiety, mood swings. Paternal side of family has history of thyroid disease: grandmother, aunt, uncle. My father, now dead from suicde, had misshapened thyroid. Also suffered depression, tremors, et al. I have asked my primary care physician to test my thyroid but he says that I am too young. Please advise.