Weird question, I know, but I have inflammation in my tonsils that prevents me from singing and I’m wondering if there’s any exercises I can do in the meantime to progress my singing until the inflammation subsides. Anything would be appreciated.
Work on your musicianship: get better at reading rhythms, piano proficiency, sight reading. Read about diction (e.g. voiced and unvoiced TH). Review meanings of score indications such as leggiero. Expand your familiarity with different styles and periods. Get to know some composers you're not familiar with. Get better at reading scores. Practice your conducting. Sightsing in your head -- imagine how it will sound. Read On Playing the Flute by Quantz. Do breathing exercises. Improve your cardiovascular fitness. Attend master classes. Go to recitals and concerts. Do relaxation exercises and find out what works best for you. Watch ballet and modern dance performances. Play an instrument. Work on your music theory. Ask your doctor if it would be helpful to grind cloves with a coffee grinder to make a warm drink twice a day.
Hang in there!
You can train pretty much all of your primary and secondary vocal musculature silently, including diaphragm, tonque and lips along with the laryngeal musculature. You can of course study your literature, learn texts, &c.
But you should refrain from actually producing sound. This will cause fast vibration of your vocal chords, which can increase the irritation or even cause injury. Also an irritated throat might lead to technically bad singing which causes more strain on the vocal apparatus.