My PubMed search revealed one case report (written in German) from 1986. According to the abstract, which thankfully is written in English, the patient developed tinnitus 5 minutes after injection which resolved without intervention within 30 minutes. I also posed your question to a well-known expert on allergen immunotherapy, Dr Harold Nelson. He indicated that he has never heard of an association between SCIT and tinnitus.
Reference: Jablonski K and Tronnier H. Tinnitus as a side effect of hyposensitization treatment. Case report. Derm Beruf Umwelt. 1986 Mar-Apr;34(2):39-41.
Jacqueline A. Pongracic, MD, FAAAAI