I don't know about poison ivy. I assume it would be similar to poison oak. Don't burn it unless you live miles away from any neighbors. Make sure you have good health insurance and a nice hospital.
It used to be that during fire season, in Northern California and Southern Oregon, somebody on a crew would inhale the poison oak smoke, and being sensitive, get a trip to the hospital for an overnight stay and treatment. One year it was a woman from our area.
If I were your neighbor, and was sensitive, and you torched it off with the smoke coming my way, well, I might be a little bit angry and phone a lawyer.
As for treating the skin eruption, there are people called doctors. Sometimes, it is wise to go see them.
I just found out that we had worked in poison oak a couple weeks ago. I am apparently still insensitive so no problems. But a guy that I worked with had an eruption from wrist to elbow, and had to go get proper medical help to start getting it cured. No bleach--real medicine.