And BTW, I usually do a second rinse when I do laundry. I use a fraction (usually about 1/4) of the recommended amount of a mild unscented detergent, and I put the clothes through a wash cycle and two rinses. If I think about it, I put some white vinegar in the first rinse. The second rinse washes out the vinegar. The clothes get clean, unless there was a stain that needed to be pre-treated.
The only thing I can add to Dr. Anitha's comments is that you might try a white shirt, to see if it's the dyes. It seems like washing several times ought to get rid of any residue of anything that could rub off on you, so Dr. Anitha's suggestion about the detergent makes a lot of sense. If you can't find any detergent that you can tolerate, you can wash with washing soda only, or even baking soda only. You can put white vinegar in the rinse water for a little more cleaning and freshening power, if you want. You usually can't smell the vinegar after the clothes have been dried. If you've tried every fabric except organic cotton, I don't know what you would have to lose by trying that, too.
Hi, organic clothing like you mentioned is more of the eco friendly type and derived from natural sources. Cotton clothes may cause less allergic reactions as compared to the more synthetic or silk varieties. You could also check to see if the detergents are causing your problem. More milder forms may be hypoallergenic. And try washing with treated water. Regards.