I too experience chronic itching, primarily on my back and in the evening. I understand that in my case this is related to the bile duct dilation. I question the use of full strength tea tree oil, but also know that the warning on the bottle I have says not to use full strength on one's face. I was prescribed a medication for my itching that came in powder form, but my pharmacist told me she did not think I would like it because it takes a long time to start working, and it also causes constipation, so I never tried it. Instead I use the prescribed cortisone ointment on occasion.
I scratch so much that I bleed often. However, the attacks are rather short and then I have to will myself not to scratch. It can be just awful. I may look into the tea tree oil, but perhaps dilute it and make a spray so I can spray my back.