As per the present knowledge, Tinnitus is caused by some problems with the Auditory nerve connecting the inner ear to the brain, and the sounds are locally generated/appear to be generated, and it is not related to the level of testosterone. Also if testosterone were the reason, all females should have got it.
Here is a reference for you:
ok what about being completely exhausted even after 10 hours of sleep?
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.
By the way, doctors shy away to find the reasons for tinnitus, as they do not have any standard cure for the condition. They at best do an auditory response test to evaluate your ear performance and just leave at that with an advise to adjust and live with it.You will get a lot of info regarding tinnitus from tinnitus.org site.