Story-time! A couple months ago, a friend and I cut down a giant white oak tree, with the same hairy vines all over it. I've never been allergic to anything like that, ever. But i guess, due to the sheer volume of ivy sap that soaked my jacket sleeves, gloves, and pants, I was bound to get SOME kind of reaction. Sure enough, about 3 days later, i started itching on my upper arms, and between my knees. Over the coming 3-4 weeks, it got worse and worse and worse. My wife got it too, and she's badly allergic. But with benadryl lotion, it went away, thank goodness.
There was so much itch juice soaked into my clothes, that even after 2 washes and drying, I wound up getting it again, after it cleared up, but it went away in a day or so.
There's my story, lol. Hope you don't itch soon. Good luck.