It is difficlt to answer this as we are not health practitioners and can only tell you what we have experienced or learned. I looked up chlorine colycistitis and, unless you had exposure to chlorine I don't understand the terms. Cholecystitis means that your Dr thinks you have an infection of the gallbladder. I don't know if you can heal an infection in that area by doing Liver flushes. It probably depends on whether the gallbladder is damaged to such an extent that it must be removed. Your Dr could give you an opinion on that. If the gallbladder is not damaged and the bile duct which empties into the intestine is not damaged then you may have an overgrowth of microorganisms in the bile system and the term used for that is a near-infection. Even tho your Dr is not supportive of Liver Flushes you may get enough information to decide the best course for you.
There are some LFs that are easier to do than the H. Clark method that Moritz uses. Do a search for 'raw egg and avacado flush' and look at Dr. Sutter's coke liver flush.