Hi,
My intuitive feeling is that low testosterone may cause lack of competitiveness in life, but not constant fatigue, but from another post of yours, I read that you also suffer from hypothyroidism, and it can definitely cause constant fatigue,
weight gain, extreme irritability, mental confusion,
low pulse rate,
low sex drive etc. Your Dr. may put you on regular intake of Thyroxine tab. to improve the condition.