Hearing damage is the most common cause, but it's far from the only one. It can also be caused by other sorts of physical damage (TMJ, blood pressure, etc.), certain drugs, and some diseases.
> diabetes, thyroid problems, migraines, anemia, and autoimmune disorders such as rheumatoid arthritis and lupus have all been associated with tinnitus
"...medicines used to treat other diseases, as well as foods and other ingested materials, can result in unwanted tinnitus. These include alcohol, antineoplastic chemotherapeutic agents and heavy metals, antimetabolites, antitumor agents, antibiotics, caffeine, cocaine, marijuana, nonnarcotic analgesics and antipyretics, ototoxic antibiotics and diuretics, oral contraceptives, quinine and chloroquine, and salicylates. This review, therefore, describes the medications currently used to treat tinnitus, including their mechanisms of action, therapeutic effects, dosages, and side-effects. In addition, this review describes the medications, foods, and other ingested agents that can induce unwanted tinnitus, as well as their mechanisms of action."
Aspirin (and NSAIDs in general) might be one of the most common drugs that can cause it (see section 2.12.7 in the paper). Table 15 lists the drugs that can cause tinnitus. The paper seems like a thorough, recent (2021) review.
> diabetes, thyroid problems, migraines, anemia, and autoimmune disorders such as rheumatoid arthritis and lupus have all been associated with tinnitus
https://www.mayoclinic.org/diseases-conditions/tinnitus/symp...
I don't find it the least bit surprising that Covid could also cause it.