He is suffering from waswaas and fears that his fast may be invalidated because of snuffing water up into the nostrils
You have done well by not exaggerating in snuffing up water into your nostrils, because the Prophet (peace and blessings of Allaah be upon him) said to Laqeet ibn Sabirah: Do wudoo’ properly, let the water run between your fingers and toes and exaggerate in snuffing water up into the nostrils, except when you are fasting.” Narrated by Abu Dawood, 142; al-Tirmidhi, 788; al-Nasaa’i, 87; Ibn Maajah, 407; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
If a fasting person rinses his mouth or snuffs water up into his nostrils and some of the water reaches his stomach without any such intention on his part, then his fast is not broken. Allaah says (interpretation of the meaning):
“And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend”
This person did not intend in his heart to do the fast-breaking action, so his fast is still valid.
End quote from al-Sharh al-Mumti’, 6/240, 246.
The best remedy for waswaas is to ignore it and not to pay any attention to it, whilst remembering Allaah a great deal, and worshipping and obeying Him, and avoiding sin.
See also question no. 1174
We ask Allaah to keep you safe and sound from the traps of the Shaytaan.
And Allaah knows best.