Are constipation and kidney pain common side effects of a liver detox diet?

Wouldn't surprise me. "liver detox diets" are widely varied and are not evidence-based medicine. Use them at your own risk -- they have landed people in the intensive care unit. Your personal physician -- who unlike an internet "independent thinker / persecuted humanitarian" is obligated by law to tell the truth -- is your best guide to health, be it liver function, diet, or whatever's troubling you now. Cheers.