Several months ago I attended a workshop given by Jamie Wallen. In his quilting studio they were accustomed to ripping fabrics for backing, but several years ago started noticing increasing problems with reactions as described here (congestion, sneezing, eyes watering, etc.). He talked to fabric manufacturers and came up with the following information. Before the economy crashed, the average shelf life of quilting fabric in stores was 3 months; now it's 3 years. Because fabric has to look crisp and new in order to sell, the manufacturers have started adding in a lot of additional chemicals to the finishing process -- Jamie said about 6 times what they used to! When fabric is ripped, all those additional chemicals are dispersed into the air. Nowadays in his studio they all wear masks whenever fabric is being ripped to protect their lungs from the additional chemicals.
A lot depends on an individual's sensitivity to chemicals. It's just that there are so many more chemicals in fabric today, there is a higher chance of reacting to one or more. The issue is most obvious when ripping fabric because so many particles are released into the air. Cutting also causes release chemicals, although probably considerably less than ripping. The OP may have just enough sensitivity to one or more of the chemicals to react when fabric is cut, but not so much sensitivity that subsequent touching and sewing causes a reaction.
I am lucky in that most of my stash is older fabric as I am not a pre-washer. If I noticed any sensitivities or reactions in myself, though, I would definitely start pre-washing fabric.