Ask Mr. Smarty Plants

When you say sweet potato vine, I'm assuming you mean Ipomoea batatas.  It originated probably in Central and South America and has been spread all over the world as people colonized new areas.  Our expertise and focus here at the Wildflower Center is with plants native to North America and this plant really doesn't qualify as such.  However, we will try to help you solve this mystery. Searching in several toxic plant databases I found only one member of the Genus Ipomoea that is listed as being mildly toxic, Ipomoea tricolor (morning glory)—ingesting the seeds produces hallucinations.

I suppose that there is a small chance that you are allergic to the plant itself.  The Botanical Dermatology Database (BoDD) reports some instances of dermatitis from contact with some members of the genus.  However, there is probably a better chance that you are be allergic to something that was on the plant.  For instance, in the Botanical Dermatology Database (BoDD) they describe a "rash and burning sensation" after handling Ipomoea pes-carprae (beach morning glory) that was infected with a rust fungus, Endophyllum kaernbachii, in the Family Pucciniaceae.  If you live near an area where Toxicodendron diversilobum (Pacific poison oak) grows and either you or your neighbors have a dog that might have spent a bit of time in it and then walked through the potato vine, enough of the oil from the poison oak might have been transfered for you to come in contact with while you were pruning the vine. Whatever the source of the rash, I would advise you to wear long sleeves, long trousers, and rubber gloves that next time you prune them.