Hello, Its said in classics- "Naasa hi Shirasodharam". That means nose( here let's consider it as Nostrils are the way to head(shiras literal meaning)
So when you put any nasal drops it directly enters head, so you feel little irritation which is normal.
Next Steps
Steam inhalation before and after nasal drops are very helpful, try it spare another five mins and try this, this will really help you.
Health Tips
you can instill 2 drops in each nostril everyday early in the morning.