Drinking alcohol is emphatically forbidden because of the evil, harm and corruption caused by alcohol. Allah says (interpretation of the meaning):
“O you who believe! Intoxicants (all kinds of alcoholic drinks), and gambling, and Al‑Ansaab (stone altars for sacrifices to idols etc) and Al‑Azlaam (arrows for seeking luck or decision) are an abomination of Shaytaan’s (Satan’s) handiwork. So avoid (strictly all) that (abomination) in order that you may be successful
Shaytaan (Satan) wants only to excite enmity and hatred between you with intoxicants (alcoholic drinks) and gambling, and hinder you from the remembrance of Allaah and from As‑Salaah (the prayer). So, will you not then abstain?”
The Prophet (blessings and peace of Allah be upon him) stated that the one who drinks alcohol and the one who helps with it are cursed, as it says in the hadeeth which was narrated by Abu Dawood (3674) and Ibn Maajah (3380) from Ibn ‘Umar (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Allaah has cursed khamr and the one who drinks it, the one who pours it, the one who sells it, the one who buys it, the one who squeezes it, the one for whom it is squeezed, the one who carries it and the one to whom it is carried.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
In Sunan al-Nasaa’i (5570) it is narrated that ‘Abd-Allah ibn ‘Amr (may Allah be pleased with him) said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “No man among my ummah drinks alcohol but Allah will not accept any prayer from him for forty days.” Classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 709.
So what you must do is give up drinking alcohol, seeking thereby the pleasure of Allah and so as to avoid His punishment.
If a Muslim makes a vow to do an act of obedience to Allah conditional upon him committing some sin, then he falls into that sin, the scholars (may Allah have mercy on them) say that he has the choice between doing the act of worship or offering expiation for breaking an oath.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (11/180): If he makes a vow, and it sounded like an oath, to prevent himself or someone else from doing something or to compel himself to do something, such as if he says, “If I speak to Zayd, then I have to do Hajj for the sake of Allah or give my wealth in charity or fast for one year,” this is an oath and the ruling in this case is that he has the choice between fulfilling what he swore to do, in which case he does not have to do anything else, or breaking his oath. So he has the choice between doing what he vowed to do or offering expiation for breaking his oath. End quote.
Based on this, you may either offer expiation for breaking an oath or you may do the act of worship that you vowed to do.
The one who is studying has to strive hard and not let himself down by falling short or negligence. Doing that should not be regarded as a distraction from the remembrance of Allah; rather it comes under the heading, “Allah loves, if one of you does some action, for him to do it well.”
But if the vow meant that he should occupy himself with a particular act of worship, and that will not affect his studies or keep him away from them, rather it will lead to him not excelling in them, then he should fulfil his vow and give precedence to what is obligatory over anything else.
It is obligatory to obey one's parents so long as that does not involve disobedience to Allah, because the Prophet (blessings and peace of Allah be upon him) said: “There is no obedience if it involves disobedience towards Allaah; obedience is only in that which is right and proper.” Narrated by al-Bukhaari (7257) and Muslim (1840); and he (blessings and peace of Allah be upon him) said: “There is no obedience to any created being if it leads to disobeying Allah, may He be glorified and exalted.” Narrated by Ahmad,1098.
If that conflicts with doing something obligatory, such as fulfilling a vow, and it is not possible to do both, then precedence should be given to what is obligatory.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said in al-Ikhtiyaaraat (p. 114): The individual is obliged to obey his parents in everything provided that it does not involve sin, even if they are evildoers … This has to do with what is beneficial for them and does not harm him; if it is difficult but will not harm him it is obligatory, otherwise it is not. End quote.
And Allah knows best.