There should not be any clear fluid dripping from the nose specially from one side only.
You must get an ENT consultation done and get done ---
chemical analysis for sugar and protein of the fluid which drips down
MR Cisternography to see for the fluid
It could be nasal discharge --but chances are less.if there is no cold
and the fluid is watery
Another possibility is Cerebrospinal fluid
which is protective fluid around brain , and this should not drip, so you need to get it ruled out.