As with all medications, herbs and oils can have positive and negative effects depending on the individual's biological makeup. So keep in mind that if neem oil works for one individual, that doesn't mean it will be ok for another.
Neem oil is a tricky plant based oil. Too much can cause irritation. I too have had personal experience with bad reactions. The hives/rashes/contact dermatitis you speak of are all forms of inflammation, which means your immune system is sensitive in return reacting to the substance.
I would try to place some Colloidal Silver , since it is something you can ingest and place on the skin. It's anti-fungal and anti-bacterial. Try it out and see how you do. It's a replacement for Antibiotics for those who have weak immune systems, so I would like to know how it affects you.