Is post nasal drip without sore throat possiblr?

It is possible.: Not everyone with nasal drip gets a sore throat, and not everyone with a sore throat gets nasal drip. Nasal drip (from front is runny nose; from back is postnasal drip) happens when the inside of the nose or sinuses waters, such as in the common cold, influenza, allergic or nonallergic rhinitis, irritants like spicy food, viral or bacterial infections like strep throat, medication effects, etc...

Yes: Postnasal drip is usually in the context of sinusal inflammation or sinusitis and/or rhinitis or inflammation of nasal mucosa. When infectious it tends to involve pharynx as well, causing a sore throat as in upper respiratory infections. Allergies, typically, may cause protracted postnasal drip that does not necessarily associates a sore throat.