If I am allergic to henna tattoos, am I allergic to real tattoos?

This exact thing happened to my brother. We went on vacation in Mexico and he got a Henna tatoo and had an allergic reaction in which the ink went through his skin into his bloodstream. My brother now is hoping to get a real tatoo; however, he found that most tatoo artists won't put tatoos on people who have any sort of ink allergy because it is a very high risk.