Welcome. Find what works for you.
People will jump in and insist that you have to cut out all the non-primal stuff cold turkey. Some people need to do that. I took it slowly like you and after 3 years, I am doing great (at 70 y.o.)
You don't have to cut out dairy unless it is causing you problems. I eat/drink lots of it.
I don't remember people describing a runny nose being part of "carb flu" but it may be. Are you, in fact, going low carb?
You should eliminate most grains completely. I do have some (organic) white rice, white potatoes and corn tortillas. Those are not terrible (and I wouldn't give them up anyway.)