|Thanks for your reply, Debbie.
I didn't post another message asking how to get rid of it (I figured Ortho Brush-B-Gone would do the trick on just about any plant). I guess I'll have to look around more carefully, then. Something in there is giving me a rash almost immediately, and I don't see anything else that's even remotely suspect. Other than this English Ivy, I only see clover, the azalea bush itself, and a few random weeds.