For those of us with sensitive skin, the sourse of irritation is usually the fragrance that the lotion companies use in their products. If you don't mind paying for it you can try kpangan butter, also known as "golden shea butter". It is similar to shea butter but leaves the skin feeling less greasy. Here is my recipe for my whipped butter hand balm:
2 part Kpangan butter
1 part almond oil (if you can afford it you can also use jojoba oil)
Melt the kpangan butter in the microwave until it is soft but not melted.
Mix in a stand mixer on high until the mixture is smooth and some air has incorporated into it.
Please use only clean equipment and utensils to avoid contamination. Remember there are no preservatives in this product so you will want to be mindful of introducing any foreign particles into your cream. For longest product life, keep any extra cream in the refrigerator.
I have made this cream for many of my friends and family members with sensitive skin and I haven't had any complaints yet!
Best of luck to you.