Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with a person using ointment to moisturize the lips or nose.
Answering your question, the late Saudi prominent Sheikh Ibn `Uthaymeen (may Allah have mercy on him) states:
There is nothing wrong with a person using ointment to moisturize the lips or nose, or moistening them with water, or with a cloth and the like, but he should avoid anything that could reach the throat.
But if anything reaches the throat without him intending it to, there is no sin on him, just as if he rinses his mouth and some water reaches his throat by accident, his fast is not invalidated by that.
Allah Almighty knows best.