My wife's hands swell up and we think it is caused by hand soap, what kind of soap should she be using?

i'm assuming that you have recently changed brands, so just go back to what you were using before. If This developed from the same soap that you have been using for a long time, then just get new soaps that are hypoallergenic. these are less likely to cause problems. everybody is different and you may have to shop around to find one that works for you. Stay away from ones that are scented of dyed.