So sorry to hear you’re not feeling well. I am better today, but had a yucky little bug for the past week, and every time I went in to work, it taxed my throat and energy and I kept relapsing.
Think of your body as busy at the moment. It has a new job – clearing out an infection/illness, and you need to assist with that. That means not challenging yourself to do something physical other than getting rid of it. For me, it’s as much sleep as possible. When everything else shuts down, the body can put all its energies into the one job. Bed rest operates on that principle.
The tons of water (I add OJ for vitamin C) is good for flushing it out as well. Plus you keep your fluids moving freely to get all body parts to do what they need to in the fight. So even though you think you’re sedentary, you’re getting a workout.
Low aerobic movement helps the blood flow and keeping your strength, so I’d say gentle treadmill walking but not real workout until you are definitely improved. I know this sounds very dull and like you’re giving in, but actually it shortens the time of illness and shelf life of germs inside. You’re a hostile host, so it leaves. When you go back to the gym, allow one or two sessions of your earlier, easier routine, then build back up. It will prevent injury.