You ask an interesting and intriguing question that is by no means foolish.
The answer I would give is "possibly".
There are a variety of tattoo inks available and the industry is not well regulated. Secondly the amount of ink injected can vary. There is a quantitative difference between a one-inch butterfly and a ten-inch dragon. Thirdly, because the inks are expensive, some tatoo artists use a common "well" from which to draw ink for several customers. And fourthly there is the issue of needle sterilization.
All tatoo inks are "antigens" or non-self substances, and all will provoke some sort of inflammatory reaction. Some inks are worse than others in this respect.
Prudence would suggest that a permanent tattoo be avoided.
Welcome to the medhelp neurology forum with your query. fibromyalgia is a chronic condition causing pain, stiffness,tenderness on muscles, tendons and joints. There appears to be a diffuse disturbance in pain perception in fibromyalgia patients. Tattooing can elicit unknown responses in these patients because about half of them are known to have allergies. It may trigger muscular pains and other symptoms in these overtly sensitive individuals. So I would advise you to exercise caution and avoid tattooing although there is no substantial proof of it being a trigger or aggravating factor. I hope this helps. Take care and feel free in contacting me again for any further clarification.