How long would it take to go into anaphylactic shock from poison ivy exposure?

Not long: Seconds to few hours, but definitely not few days . But anaphylactic shock is extremely rare from exposure to poisonous plants, more common reaction is contact dermatitis.

Not related: Poison ivy is a different type of allergy. It is a rash that starts 12-24 hours after it touches your skin and worsens up to 48 hours later. It does not usually cause anaphylaxis . Those who are sensitive have activated their immune cells to kill any of your skin cells that have been contaminated by touching the oils of the plant.