Don't worry about it!
when you are sick your health comes first. It is highly likely people who are on this plan will get sick. The stress our bodies go through on this diet can make some of us more likely to fall ill if exposed.
As Linden says, "eat what you can keep down." Stay very well hydrated. Just avoid juice. Decaffeinated herb teas are great for this. Also, some of the herbal teas are specifically formulated for cold/breathing/flu/sore throat symptoms and are helpful.
It is good to know ahead of time that you can use diet ginger ale. You can make a homemade fresh ginger tea. You can use a low sodium low carb chicken broth. You can use any of the IP soups, keep a few on hand even if you hate them.
I ate boiled chicken breast and boiled ground chicken breast when I was sick.
If you get medicine, make sure your doctor writes for a diabetic or sugar free option if it is available. THEN make sure that is what the pharmacist filled.
You can use sugar free cough drops and cough syrups. Make sure they do not have maltodextrin if you can avoid it. This particular sugar alcohol actually activates insulin production.
Feel better soon.