This sounds like a case of contact dermatitis, probably related to the chemicals used in the manufacturing of the plastic. Some people are just sensitive to any of the many chemicals used; however, I am increasingly seeing bad reactions to manufactured goods, especially to those made overseas. Not every country has the same safeguards we have in place in North America.
Some of these chemicals are volatile and disappear after a short while. It's possible that washing the glasses in hot, soapy water could have been able to remove them. However, in your case, the reaction was so strong that I would avoid that brand in the future.