I know people hate to hear this because it sounds dismissive, but I'm going to say it anyway. I really believe that if you do not have any burning sensation of mucus membranes then the problem is mostly psychosomatic.
I'm not dismissing the problem. I think many people are taught, no not taught, they have it drilled into them, how dangerous lye is, how it will burn them with 3rd degree chemical burns if they even get a drop on their skin. Then they go to make soap. Again they are warned to wear full length garments, eye protection and heavy gloves. They are told to mix outside or in full ventilation because of the fumes that omit from this vile mixture.
Is it any wonder at all that if someone feels the least bit ill they think it must be the lye?
I'm not discounting the danger of lye. However I can tell you I have spilled lye water on my arm. I did not panic, my arm did not fall off, I rinsed my arm under cold running water wondering when it was going to start burning a hole through my skin. It never did. I rinsed my arm within maybe 20 second of getting splashed. The worst thing that happened was it was a slight pink spot, and it itched a bit.
This doesn't mean it isn't dangerous, and it doesn't mean it can't hurt you. Also you should always use gloves and eye protection, but lye is like any other dangerous substance. You need to respect it and be aware of everything you are doing when you use it.
I believe people are sometimes taught to be so afraid of lye that they are sure it will do them harm even when used responsibly.