Is there anything I can get from the grocery store or drug store for my atopic dermatitis until I can see a doctor?

Yes. Use skin cleansers instead of soap for washing or bathing. You can get cetaphil moisturizing cream, cerave, eucerin and the like . You can apply otc steroid creams till you see your doctor, moderate to severe eczema needs a stronger steroid cream and close follow up. Be sure not to get infected.
Yes. Aquaphor, aveeno, (oatmeal) calendula, jojoba oil, and any other thick cream that has no fragrance can help hydrate the skin. Fish oil pills can be helpful taken orally as well. Over the counter steroid cream can help decrease itch and redness as well. Eliminate dairy from your diet and gluten as well as both can contribute to symptoms. You can always add them back in if there is no change in 4-8 weeks.