I'm not saying that Milk Thistle would't do any cleansing of the liver (if it helps the cells regenerate they would probably clean them selves in the process), and I don't mean to sound like I'm challenging your statement that your liver is congested. Milk Thistle is usually recommeded more for protection and regeneration.
I guess it depends on what is meant by cleansing. There are other herbs that have "lithotropic" (stone breaking)or "deobstruent" (obstacle removing) qualities as part of their strengths. These seem like they would be more helpful in clearing/cleaning a bile duct versus cleaning a cell.
Perhaps your advisor wants you to build up your liver strength before you clean the stones out?
If you are looking to expel stones from the bile ducts, the method you have described sounds a lot different from the methods others are using with success. Each body is unique. Follow your inner voice. I'd recommend reading Andreas's Amazing Liver Cleanse book if you are looking to expel stones.