Fasting in fulfilment of a vow (nadhr) takes precedence over fasting six days of Shawwaal
First of all you should fast the remaining days of the vow, then fast the six days of Shawwaal if you are able to. But if you do not do that, it does not matter, because fasting six days of Shawwaal is mustahabb (encouraged), not obligatory, whereas fasting in fulfilment of a vow is obligatory. So what you must do is start with that which is obligatory, before doing that which is naafil (supererogatory). If you intended to fast consecutive days and vowed to fast fifteen consecutive days, then you must fast those days consecutively, and it is not permissible for you to fast them separately; rather you must fast them consecutively, and the previous fasts don’t count.
But if you intended to fast them not consecutively, then you must fast the remaining five days, in sha Allah, and that will be the end of the matter.
But you should not make vows after that, because making vows is not appropriate. The Prophet (blessings and peace of Allah be upon him) said: “Do not make vows, for vows do not ward off anything of the divine decree; all they do is get something out of the miser.”
So vows should not be made, by one who is sick or anyone else. But if a person does make a vow to do an act of obedience to Allah, such as prayer and fasting, then it becomes obligatory for him to fulfil it, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever vows to obey Allah, let him do so, and whoever vows to disobey Allah, let him not do so.” Narrated by al-Bukhaari in as-Saheeh.
So if a person vows to fast a certain number of days, or to pray two rak‘ahs, or to give a certain amount of money in charity, he must fulfil the act of worship he vowed to do, because Allah praises the believers by saying (interpretation of the meaning): “They (are those who) fulfill (their) vows, and they fear a Day whose evil will be wide-spreading” [al-Insaan 76:7].
Moreover, the Messenger (blessings and peace of Allah be upon him) enjoined fulfilment of vows, as in the hadeeth quoted above. However, the hadeeth indicates that vows are not a means of recovering from sickness or getting one’s needs met, so there is no need for vows. Rather a vow is something that a person takes upon himself, and it is a means of getting something out of the miser, but then he regrets it and finds that he has put himself in a difficult situation, and wishes that he had not made the vow. So Islam – praise be to Allah – brought something that is kinder and more beneficial to people, which is the discouraging of vows. End quote.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him).