Oh, my that has to so hard! I would say allergy shots for you and yes bathe Jess once a week with a shampoo that you are not sensitive to. It is best to keep him out of your bedroom as this is where you spend most of your time. An air purifier would also help in your bedroom. I hope your daughter will take on the responsibility to give you some relief.
My oldest son has terrible allergies including severe asthma. After a visit to an allergist and skin tests to determine what he was allergic to.....dust mites, cats, pollen & molds. We ended up totally stripping his bedroom of carpet, toys, curtains, mattress, pillow and only a sheet and blanket on the bed. New pillow and a water bed made a world of a difference! His asthma attacks in the night were so much fewer! 3 of my 4 kids have allergies.....2 w/asthma, 1 also has eczema and 1 has allergies to medicines and wasp/bees...she has to carry an epie pen and has ended up in the ER so close to her throat closing! It is so scary!
I wish you the best of luck!