This is a little late, but I'm new here...
For another base other than a petroleum by-product, use coconut oil. There are two kinds--one melts at body temperature, the other lower. warm til it melts and add essential oils (be careful, use sparingly), or steep herbs in it and strain. It will re-solidify when cool. If you want to carry it in your pocket, add in some beeswax or it will melt and run all over.
Goes on like silk, has lots of EFA's that are good for sensitive skin. Herbs to steep include rosemary, chamomile (the best), sandalwood, and calendula. Try a drop each of lemon and lime essential oils per ounce of coco oil for something really yummy.
You can also use full-fat coconut milk (from a can is fine)as a bath additive or lotion if your skin is dry and irritated.