Stop the antihistamines because you build a tolerance and they lose their effectiveness - they should really only be taken in one off situations, not regularly(can't actually tell from your post if you regularly take them or just sometime take them).
Air purifiers won't suck up any macro objects like dog hair more than a few inches from them, so you probably want to invest in a vacuum with a built in HEPA filter(i can recommend the dyson gen5 detect, but it is quite pricey)
Also I would check your filters on your HVAC, and get an indoor air quality monitor.
It's also possible you're allergic to something in your house, like mold, or your dog.