Anxiety and T go hand-in-hand. I know this from my own experience. Long-term untreated anxiety and/or depression have a direct correlation with T. I'm new to T. If you're looking for a medication that has zero chance of ever effecting your T in any way, you won't find it. You can literally put in any medication followed by the word 'tinnitus' (or any other ailment, really) and you will read horror stories. This prevented me getting the medical help I honestly needed. And a medical professional is much more qualified to answer any questions or concerns you have re: medication than me or anyone else on this site.
You're best to speak to two types of professionals (which I did, after going through several GPs, doctors, and ENT). Firstly, a psychiatrist who can evaluate your mental state and talk you through the best treatment option. Secondly, an audiologist or hearing therapist who specialises in tinnitus. Have them know each other (exchange their emails; your psychiatrist will likely want to do this anyway, so they are on the same page). You will perhaps be given medication in the short-term, other medication perhaps for longer-term, and recommended for cognitive treatment for long-term. It's not for everyone here, but I have Valium (Diazepam) if I get really bad. In the beginning, it saved me. Knowing it's in my cupboard is reassuring. I'm also on two different medications and they are monitored, along with cognitive treatment I am starting with a hearing therapist specialising in tinnitus. It's a long road, but the road does have an end. You just have to stick it out. The common theme you will find in the success stories here is positivity. The brain's plasticity needs a positive attitude and outlook. It can be difficult, I know as much as anyone, but tell yourself it even if you don't feel it. Good luck and God bless your recovery!