Yes, they did! It wasn't called tinnitus until the mid 19th century and my focus is on 17th/18th c. medicine, but John Moyle talks about it in his 1693 book on sea medicine, Chirurgeous Marinus [Which basically means 'The Sea Surgeon']

"But if there be a noise in the Ears like Singing of Grashoppers, then that is Wind and Water from coldness and moisture of the Brain. In this case, drop into the Ear a little warm Ol. Terebinth. [turpentine] and stop the Ear with Cotton, or black Wool, (as before) and decoct Jews Ears [Auricularia auricula-judae - a fungus that grows on wood] in White wine, and let the Patient drink the Wine, and do you apply the Jews-Ears warm to the Ear of the Patient; and this will help the singing and deafness, if repeated some time." (Moyle, p. 244-5)

I've not seen anything about ear plugs being used, other than in a medical context like above. The connection between loud noise and deafness may not have been well understood. (I've not seen anything mentioned about it, which isn't to say that someone didn't make the connection.) Earplugs are mentioned again in another of Moyle's book where he talks of treating deafness.

"If the Deafness be not Natural, but come accidentally, and yet there be no stoppage by ear-wax, then spirit Otalgicus [a Spirit of Wine thought to help Hearing] dropt warm into the Ears morning and evening and Muskified Cotton after it, is the best of Remedies: But if the Ear be stopt with hard wax, then put oyl of Camomil into it two or three times a day, for 2 or 3 days. At last take warm White Wine, and syringe it often and forcibly into the Ear, and there will come forth a lump of hard Wax out of the auditory passage; then stop the Ear with the Spiritus Otalgicus and Muskified Cotton, as before..." (John Moyle, Abstractum Chirurgiae Marinae, p. 78)

As a follow up question - how common were earplugs in the 1800s? Wax earplugs are mentioned in the Odyssey (to avoid the Siren's calls) but not sure if their use was common or not until the 20th century and couldn't find anything that covers the history of earplugs pre-20th

As tinnitus is mentioned, I hope it is OK to mention that anyone attracted to read this because of the tinnitus element should check in with /r/tinnitus after seeing a dr ofc..