That sounds familiar. Buy lots and lots of hydrocortisone cream, you'll be needing it.
When I went around the yard actually looking for poison ivy, I was amazed at how much there was. Virtually every shady spot was covered in it. A few sessions with Roundup has lessened it somewhat.
If you have some large trees in or near your yard, look for heavy vines that are brown and "hairy" growing up their trunks. Carefully examine the leaves on those vines. That's not okra you're seeing. :-)
Our subdivision has about 15 acres of common-area woods. It’s full of poison ivy! It was in the upper 70’s earlier this week, and I think the gang of 6-10 year old girls decided to play Indians or Dryads or something, and went flitting through the trees.
I haven’t checked on their friends, but I doubt my girls are the only ones paying the price! We’re using “Ivy-Dry” and giant antihistimines.