Are you sure your dog is full poodle? I only have reactions to my standard poodle when he has been playing with other dogs, even doodles, and have to shampoo him before I can be around him again. Also, shampoo for sensitive skin may not be enough. Make sure it has zero chemicals, and do not use any conditioner. I have found Earthbath has worked the best for us. When I forgot to take it with me for the groomer to use last time I had a problem even though they had used sensitive shampoo.
I also have a reaction to house dust. I finally had to hire someone else to do the vacuuming and leave the house for 3 hours for any dust stirred up in the air to settle before I can return. Another problem was dog food and treats that released any dust, he is now only fed raw, and single ingredient raw treats so either dried meat or vegetables like sweet potatoes, etc. Also, making sure that any bedding has not been treated with chemicals, or anything like scented laundry detergent. Even dryer sheets affect me. I had to re wash my sheets once three times after a friend kindly washed my sheets and used dryer sheets. I keep re-reading the posts about the seriousness, and death. Sadly sometimes it is a choice between a pet and a person..... .. Blessings, and hoping it works our for you all