If you google up dog allergies you'll see that they tend to show different symptoms than we humans do. More itching, losing hair but also runny eyes, noses and clogged up ears. It does sound strange that only one nostril is dripping. Not to say that it can't be so but having read some posts here of folks finding weeds, particularly foxtails (? not had them may have the name wrong) I think that would be worth investigating further.
My boy's allergies did seem to be seasonal/environmental. He was itchy. Some holistic Vets now believe allergy symptoms are rooted in gut issues and when an acute gut issue did appear, was treated and fixed my boy's itching stopped. So for him it does seem to be true. Blood testing with a Vet familiar with what to look for in gut issues is an option for suspect allergies but as I said above, you might want to look further up that schnoz first. Good luck.