I've had loud tinnitus in my left ear, caused by hearing loss, for about ten years now, and it's been a cause for a good deal of despair. While I don't sit regularly due to certain fears, emotional issues, procrastination, etc., at the same time I do consider meditation to be of profound importance in my life. I suppose I'm just not there yet, and for now I study the suttas, work on my sila, and listen to the talks of various bhikkhus. Anyway, last fall I wanted to know for certain if I could still reach a degree of concentration with this constant ringing. It just took some strong viriya, and ananpanasati. I found that the ringing did not prevent me from reaching a state of concentration. I don't know if this ringing will be a barrier for me later on when my goal is jhana, but my assumption is that it will not be. (I reached jhana in 1994 after a few weeks of many hours of sitting before I knew anything about jhana. (At the time the experience really frightened me and left me with some lingering fears about dying in meditation.)
My suggestion to overcoming tinnitus is to cultivate the conditions for strengthening viriya, and to persist. Your tinnitus can't be any more pernicious than mine. And I've lived a pretty dissipated life until quite recently. In other words, if I can do it, you can too. Don't despair. It might take a month or more or sitting/walking meditation, but you will get there.
Rain soddens what is covered up,
It does not sodden what is open.
Therefore uncover what is covered
That the rain will not sodden it. Ud 5.5