I found this on an opposition site. Unless the discharge turns milky or yellow/green I'd suspect an allergy.

It's a Spring too so the perfect time for allergies to surface! So too there are always so many allergens in the house too, even things like dust mites. Allergies do take some time to develop depending on the allergen.

The dogs do sound like a reasonable culprit too.

ALLERGY
Lasts longer than a week or is recurring
Usually no fever
Nasal discharge is thin, clear & watery
Sneezing frequently or in bursts
Blocked nose
Watery eyes
Itchy, rather than sore throat
Itchy eyes, nose, throat


COLDS
Usually lasts up to a week
Sometimes mild fever
Nasal discharge is thick and cloudy, perhaps coloured
Infrequent sneezing
Blocked nose
Unlikely watery eyes
Sore throat
Unlikely itchy eyes, nose, or throat