All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Your mother must take these drugs if not taking them could increase her illness and deteriorate her health. As Allah Says (what means): {And do not kill yourselves (nor kill one another). Surely Allah is Most Merciful to you).} [Quran 4:29]. Moreover, ‘Aa’ishah narrated that the Prophet said: “Whoever has made a vow to obey Allah, he should comply with it and whoever has made a vow to disobey Allah, he should not do so.” [Al-Bukhari]
Therefore, your mother should expiate for her oath if she takes the drugs as Abu Hurayrah narrated that the Prophet said: “Whoever makes an oath to do something and finds another thing better, he/she should do what is better and make an expiation for his/her oath” [Muslim]
The expiation of the oath is to give out a ration of food to ten people that is sufficient for each one of them as one meal. The food should be from the average food - as far as quality is concerned - eaten by the family of the person who has made the oath, or clothing ten people giving each one of them a cloth, or to free one Muslim slave. Whoever does not find any of these, he should fast three days as expiation, as Allah Says (what means):
{Allah will not impose blame upon you for what is meaningless in your oaths, but He will impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] — then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths. Thus does Allah make clear to you His verses [i.e. revealed law] that you may be grateful.} [Quran 5:89].
Allah knows best.