He is suffering from waswaas and fears that his fast may be invalidated because of snuffing water up into the nostrils
Question

                I am (may Allaah heal me) one of those who are affected by waswaas (whispers from the Shaytaan). When doing wudoo’ whilst fasting I try not to exaggerate in snuffing water up into my nostrils, but I feel something in my throat. Is my fasting invalidated by that?.
Praise be to Allah.
      Firstly: 

    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.  

    Secondly: 

    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”

    [al-Ahzaab 33:5]

    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. 

    Thirdly: 

    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.