I was going to suggest what Kent did, for ID.
There are SO many plants that can cause a rash, but the poison ivy/oak/sumac gets most of the attention because they can cause their misery from very slight, casual contact with unbroken plant parts. That's pretty a pretty rare thing for plants to do, and Ailanthus isn't in that category, that I've found. The anecdotes are about exposure to sap. Have you been molesting Ailanthus (trying to remove it, pruning?)
Have you been propagating &/or pruning other plants? The sap of so many plants can be caustic, for the unfortunate few unlucky enough to be sensitive to the alkaloids in them. Since that sensitivity is pretty rare, coupled with there needing to be coincidental molestation of plants by the person who happens to be sensitive, that kind of thing is hard to research, and not much understood in regard to a lot of plants. If you've been exposed to plant saps, it might help to list them here. I'd be happy to let you know if they are ones I've encountered in my long, exhaustive search to figure out why I kept getting "mystery poison ivy." Turns out, the sap of many yard plants & many of my house plants are caustic to my skin.