When you have allergies, eczema or any other type of medical issue, it's always a good idea to carry along the essential items that you may need. Along with my bandanna to prevent myself from touching nickel found in doorknobs and such, I also carry a bar of Dove Gentle Exfoliating Soap inside a travel case.
I ALWAYS have this black 100% cotton American Apparel bag in my purse. It holds all of the essential things I need to get through the day:
I've got lipsticks, lip glosses, eyeliner and blotting papers for a quick freshen up... some steroid ointment if my skin is breaking out badly and last but not least... a little tube of antibiotic ointment. The antibiotic ointment is extremely important since I'm allergic to ALL over the counter topical antibiotics.
In my handy dandy bag I also have some hair bands and clips. If I have eczema on my hands, I really have to watch out when it comes to handling hair bands. The synthetics tend to irritate my skin if it's in a sensitive state. Good luck finding stretchy cotton hair bands! I'm pretty sure those don't exist. Cotton isn't an ideal fabric for everlasting stretch.
I also carry around a handy dandy Allergista compact mirror ;-) It's great for touch ups on the go!