Hi @mrpetrov im sorry you're going through the same symptoms they are truly awful and standard tinnitus pales in comparison. I don't sleep with any noise generally as you say it just aggravates it and wakes me, many times I'll wake up at 4am with my beeps going in overdrive and almost wake up in a panic attack, it's not easy.
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I try to tire myself out of a day through long walks and just tried to get back into the gym so I'm literally exhausted. I've tried various sleeping medications which all work but leave me groggy next day. The only one that doesn't is ambien and that isn't something you want to be taking everyday.