I take them out of the dryer while still fairly damp, then iron. If they get a little too dry in spots I spray them with a mist of water. I don't have a problem with serious wrinkles except for flannels. I never get all of the wrinkles out of them.
Oh, I forgot, put your dryer temp on low heat.
Sorry about the allergy to the chemicals. Formaldehyde is a beast! But it CAN be washed out. It just takes a little doing.
Good luck! 8-)