Don't overthink it. You're just building rapport, and escalating towards a date. Her being sick is an opportunity to show her you're compassionate. I might say "Now it's you who wishes we were dating. I make a mean chicken noodle soup." But I don't think it really matters that much. Get the convo going but dont get pushy on setting a date soon because it would show that you're not recognizing what she's telling you about her health

This is not a shit test. Just wish her well and tell her to feel better. "Damn, that sucks. Feel better soon"