The water from my kitchen faucet and from my bathroom faucet are the same or not?

Unless your home is extremely unusual there is one water supply line coming to your home. All the water in your home is supplied by that line. The water in the kitchen is the same water as in the bathroom. If the water in the kitchen makes you ill then drinking water while taking a shower would have the same effect. Many communities put chemicals in the water to control bacteria. It may not be so much the water, but you may be allergic to the chemicals being used. You might want to contact your physician and explain what is happening. Good luck.