Why does my right side of my nose twitch?

Myokymia?: Random twitching of an eyelid or another small facial muscle, which happens in normal people, is called myokymia (an involuntary, spontaneous, quivering of a few muscle cell bundles within a muscle). Myokymia starts and stops spontaneously. It can last a few minutes to a few days. One should see a doctor if such symptoms persist, keep recurring, or are combined with any other symptoms.

Facial twitching: The face is full of small muscles that control our expressions. Some of these muscles are attached to the nose, and when contracting, move the nose a bit. Muscles anywhere can twitch and facial muscles cause facial twitching. If it is significant enough, you can consider using a tiny amount of Botox to quite the muscle down a bit. Hope this helps!

Muscle spasm: The small muscles of the face can spasm at any time. When the eye muscles spasm its called blepharospasm, the lip muscles can spasm as well as the nose. These spasm usually come and go. At times they can last for days or more.