What is causing my months long dry cough with no real symptoms other than itchiness/irritation in the back of my throat?

Allergies/LPR: Allergies cause the typical nasal congestion, runny nose, sneezing, and watery eye symptoms. They can cause irritation or itchiness in the throat, as well as, a dry tickle cough. Laryngopharygeal reflux is often associated with a dry cough. You should get evaluated by ENT doctor who does allergy testing and also get a detailed head and neck exam to check your throat for other potential problems.