It is NOT a chemical burn. It's an activation of TRPV1 receptors. Normally these receptors activate due to increased temperature, capsaicin activation means they think there's literally an increase in temperature. They THINK you're burning, but you're not. There's no chemical burn; it's reversible and generally safe with no lasting damage.
Your fat soluble comments are accurate, although it's really time more than anything else that will alleviate the pain. You do not need to soak your hands in oil before washing, not sure where you got that from. Soap and water works fine.