Does using a gel ointment through the nose break the fast of one who is fasting?

If the nasal ointment reaches the throat or stomach, the fast is broken. However, if none of it reaches the throat or stomach, the fast remains valid. The proof for this is the hadith (definition): "And exaggerate in sniffing water (during ablution) unless you are fasting." Therefore, if what is used in the nose does not reach the internal cavity (stomach/throat), then there is no harm in it, and it only dissolves in the nose. If something reaches his internal cavity unintentionally, then there is no blame on him.