Dear Kari,
I feel so bad for you daughter! I was the poison oak queen of all time when I was a child and I suffered so much.
I was so allergic I had to take pills every summer because I would break out without even going near the stuff. Tecnu soap and things like that never worked for me.
Poison oak on or near the eyes is very serious!
Get your daughter to the emergency room.
NEVER put her in a hot shower. She needs a cool bath with oatmeal and/or baking soda. My mom used to strip me naked and put a baking soda paste all over me and wrap me in a cool towel. That helps on the body and perhaps on the cheeks, but you don't want any baking soda getting into the eye.
The doctor can give her a shot and I also had to take steroids which is not as scary as it sounds. It's less dangerous than just leaving it alone or running hot water on her. Your daughter needs immediate medical attention.
The good news is, I haven't had even a tiny patch of poison oak in over 10 years and no longer need the pills. I can go hiking and berry picking with my son and be 3 feet from poison oak without getting it.
For now, you've got to get her out of misery and get her eye checked. You also want to avoid the possibility of scarring.
My heart really goes out to her. Let us know what the doctor says.
Best wishes!