I can attest to itching due to backed up bile. I got Intrahepatic Cholestatis of pregnancy and I had the worst itch you ever imagined in your life. My liver enzymes went up and the bile acids in the bloodstream drove me bananas. I had to be taken off from work as I couldn't sleep at night.
My condition was caused by pregnancy and thought to be due to either bile obstruction, or the liver simply giving out because of the overload of estrogen hormones.
But you mentioned HCI, and I remember a little while ago clearing all of my eczema problems when I supplemented with HCI.
I think I might try that again, along with the MSM and SAMe I was taking.
