Constipation,bloating and insomnia are classical die-off symptoms.
I find that "detox bath" really help!(sweating for 20 minutes!)
For constipation increasing the amount of good fats(avocado, olive oil, flax seed oil) is important as well as increasing the amount of magnesium.
If you still have problem going to the washroom, it might be your liver's capacity to get rid of the toxic load that is exceeded. In that case, adding gentle herbal teas (nothing too harsh that has habit forming ingredients like sene) may help a lot . Exemples are, artichoke tea, cherry stems....ask your local health food store.
It is very important to "eliminate" toxins through detox pathways (urinary, colon, skin) if you want to get healthyer!