Systemic reaction from laser tattoo removal. What caused this reaction?

It is difficult to say without photos. I recommend getting a formal evaluation with a laser tattoo removal expert. I also suggest the PFD patch in the future. Best, Dr. Emer 

First, let me say that any number of things coincident with your tattoo removal treatment could have touched off your reaction. BUT...
It’s also entirely possible it was from your laser treatment. You didn’t mention colors in your tattoo, but some reds and blues can get unwanted attention from your immune system, and those probably aren’t the only colors. It makes sense that it would happen now and not when you got the tattoo: allergy requires pre-exposure and sensitization. So getting the tattoo was the primary exposure, and the sensitization (when you “became allergic”) happened after. Then your treatment may have released ink allergens from their protected environment in your skin. I’m not saying this is exactly what happened, but it’s entirely possible. 
I would stop all treatments unless (possibly) under the VERY watchful eye of an allergist. Your next reaction could be even worse. The same goes for new tattoos. It’s just not worth the risk.
Thank you for this excellent question.