Hello! After a thorough review of your statement, I would like to suggest the following --
1) A rise in the cholesterol
levels per say does not cause itching!
2) The cause of itching in your case apparently seems different.
3) So, I would suggest to have consultation with an eminent dermatologist
for further investigations & treatment of your problem, as a concomitant disease like obstructive jaundice
must be ruled out or it may be a simple cause!
So you need not worry at this stage.
Thanks & wishing you a good health!