Chemical engineers make the world go round! I dont work with plastic molding, but my company does make air filters for the kinds of chemicals you are smelling.
If your shorts are giving off enough gases to make your eyes water then send them back. Lots of plastics off-gas, but a new pair of undies shouldn't stink bad enough to (literally) make you cry. Not all VOCs are toxic, but many of them are skin/eye irritants... so why run the risk of long terms symptoms by exposing yourself to it for hours at a time?