Is there anything I can get from the grocery store or drug store for my tonsillitis until I can see a doctor?

Other than pain meds. Other than pain medication such as ibuprofen, tylenol, (acetaminophen) lozenges and gargles, there is no cure otc available. You need to determine if you have strep, requiring an antibiotic to prevent serious complications.Call your doctor.
See your doc ASAP. Tonsil infections can be viral or bacterial and it is sometimes difficult to tell (especially early on). Providing you do not have a high fever or have significant difficulty swallowing or breathing then you may temporize things with ibuprofen, tylenol, (acetaminophen) sore throat lozenges, and/or warm salt water gargles. If these fail to respond and breathing issues develop head to the er!