Cyrulis
I make kefir from both, raw and cooked in small and in big amounts at a time. Sometimes up to 1.5 liter in a few minutes. Alone and with food. Strong and mild. Cold and warm. Never had red face, constipation (because of kefir) or anything like that. You just might be alergic to milk or your dosha disagree with kefir. If neither is true, you just might have die off and you know when bad guys are dying, they release quite a bunch of gases and chemicals, hence the constipation.
My benefit nr.1 because of kefir- very good elimination, nr. slightly increased energy.
One more thing. Theoretically, if you are of asian descent, your body maybe reacting to alcohol either in kefir itself or to alcohol when dying bacteria release, as you know, asian people often lack an enzyme that efectively metabolyzes alcohol related compounds in the body.
If not, try on a very small amounts and increase little by little. And to try using goat milk is a good idea. Just make sure you get new grains for goat milk for you cannot culture grains in any other milk if you started in cow's milk.