Next time s/he tries it on like that you simply email back a one sentence reply. "Thankyou for your concern." Don't respond to any more details such as specific tasks s/he wants you to do, just the reply "thankyou for your concern."
It heavily gets your point across but s/he couldn't accuse you of being rude or not responding to emails. Keep a record. It's unreasonable behaviour.
There is only so far I'd go. I work in a primary school so everyone goes in sick all the time as we're too stretched for staff as it is. Primary schools are a germ fest anyway so you'd never have people in if you stayed off with every sickness you got. So we only stay off if we seriously need to, and we all know that colleagues must be feeling bloody terrible if they're not in as none of us like to leave the rest of us in the lurch, or the kids for that mattter.
If I have vomited or feel I'm about to, I stay off. If I just have the start of a stomach bug and have stomach pains and feel off/no appetite, I go in till (if) it gets to the "feel bloody awful" stage. If I'm just feeling a bit shit with a heavy cold and/or sore throat and a mild high temp, I dose up on Anadin Extra and go in. I've had COVID a few times now and the bad times were very bad and I stayed off. If I have a migraine (not often anymore but used to) where I feel nauseous, can't think or see straight, I stay off.
Basically if I can dose up and manage to do the job, I go in. If I can't manage to do the job, what's the point in me going in, so I don't.