a lot of tattoo inks use very small amounts of minerals, metals, organic substances and chemicals in the manufacturing of the tattoo ink, which create the desired pigment of each ink color. some metals used could include antimony, arsenic, beryllium, cobalt, lead, lead compounds, nickel and selenium, collectively referred to as toxic metals.
i've known of many people whos bodies reject or react to metal jewelry, but have gotten and healed a tattoo just fine. you may be surprised to find out that the most common allergic reactions from tattoo inks occur from using organic inks. actually if you really think about it, it's not much of a surprise, but often over looked. i have never personally tattooed using organic inks, but some artists at a shop i used to work at bought a set and while most tattoo ink bottles come with warnings, organic inks such as "eternal ink" have each and every bottle labeled with a large warning. someone allergic to such inks might have their tattoo "bubble over" and turn white, scar and fade in some places, but if taken care of well, can still be saved in the healing process and gone back over later with other inks. your best bet is to ask your artist what kinda of inks he is using. i noticed you said you are getting a black and grey tattoo, so as far as your allergies to metals, you should be fine, but if you wanted to take that extra step now that you know about organic inks, keep in mind that every artist does black and grey tattoos diferently. some artists use the obvious black ink, then tones of grey wash, while others use black ink, less amount of grey wash and then actual grey coloured ink, which could potentially be organic. but that's just eztra info for you, if all you're allergic to is certain metals. you should do fine i think, and i hope all goes well!