The adhesive in duct tape definitely can cause immune system reactions. There was the amusing (and peer-reviewed) article some years ago* that duct tape over planter's warts was as effective as the standard treatment (applying acid for a few weeks). The theory is that the irritation and reaction caused by the duct tape mobilized the immune system to that location and cleaned up the warts. It wasn't 100% effective, more like 50%, but that equaled the gold standard treatment at a much lower cost and much greater accessibility.
*my wife is an MD and so the magazine rack in the bathroom is full of New England Journal, Annuals of Internal Medicine, etc.
In my own professional work (environmental engineering), I have found that the chemicals in tape adhesive vary widely from manufacturer to manufacturer and differ as the product ages. Also, clearly, we each have individual sensitivities to toulene and other volatiles used in those adhesives.