Use a grocery store that offers curbside pickup. I did this when my two kids were recently sick with a flu-like illness, and I didn't want to bring them into the store. For an extra charge of $6.95, I ordered the groceries online, and then just pulled into the parking lot at the assigned time, and let the attendant put them in my trunk. This way, no one else was exposed to my kids' illness, and we got the supplies we needed. I was also able to pick up some additional items, like snack foods and magazines, which helped pass the time until they got better.
Call your local pharmacy and ask them to allow you to purchase what you need through the drive-thru window. I did this when my daughter got the chicken-pox as a toddler. I knew she was far too contagious to bring into the store, but I needed to pick up some anti-itch cream to help her feel better. So I called the pharmacy and asked them to please bring the items I needed to the drive-thru window. They were happy to oblige, and were probably glad that I made an attempt not to contaminate anyone.
Use a grocery service that will deliver items right to your door. There are several national grocery delivery services that you can use, including Peapod, Netgrocer, and We Go Shop. Again, they will usually charge a delivery fee, but it may very well be worth the peace of mind you'll gain from knowing that you can get the supplies you need without having to take your sick child out to run errands.