There are some drugs (I am thinking about legal ones) that are known to have the potential side effect of causing tinnitus. Aspirin is near or on the top of the list. I attribute my own tinnitus to taking a lot of aspirin when I was younger, and also wearing inadequate hearing protection during exposure to a lot of loud noise while I was employed as airline mechanic.
As far as lack of sleep and tinnitus, I was halfway watching an educational program a while back ago (I say halfway because I was doing something else at the same time--therefore I won’t swear I’ve got this part correct) and what I think I got out of it is that the sleep deprivation-tinnitus correlation is that tinnitus can result in poor sleep, not that poor sleep results in tinnitus, and that certain other health conditions that people with tinnitus are afflicted with are due to the chronic lack of sleep.
But, if I didn’t learn anything else during my next and last career as a nurse, I did learn that healthcare and medicine are not exact sciences.