Yes, milk thistle is great. Alkalinity is ultra important. But I'm not sure cutting out all Sugar (except of course added in sugars like fructose & table sugar) & milk at the same time as doing parasite killing is a good idea.
I have been experimenting with the paleo diet. It usually means no Sugar (though you could get them from carbs off the paleo diet) and no milk. That has die off too! I have gotten headaches, fatigue, shakiness. It would not be good to compound those problems with the die off from parasites.