Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The Hadith you are asking about is reported in Sahihain with the words: "When the month of Ramadan comes, the gates of Paradise are opened and the gates of the (Hell) Fire are closed, and the devils are chained." [Reported by Imams Al Bukhari and Muslim]
Qadi Iyadh a known scholar said: 'The Hadith points out the great reward and forgiveness that a person gets in this month and that devils’ mischief decreases much as if they were put in chains.'
Al-Mubarakpoori reported in Sharh al-Tirmizi from al-Qurtubi that he said: 'If one objects saying why do we see evil and sins happening in the month of Ramadan while the devils are chained, the answer is that the ratio of sins falls a noticeable level from those fasting persons who adhere to fastings rules and do not violate the etiquettes of fasting on one hand and fulfilling its condition and other recommended matters on the other. The Hadith does not prove that evil and sins disappear totally in this month since the evil happens for many reasons other than the devils such as bad habits, bad people, etc.'
Therefore, it is not astonishing to see someone getting involved in magic or committing sins during the month of Ramadan. However, the problems you are facing may not be due to magic. The person who does not fast and does not follow the religion is more vulnerable to magic and other kinds of evil acts. So, we advise you to keep on performing prayers and reciting the supplications.
Reciting some portion of Qur'an to seek cure is recommended since whole Qur'an contains Shifa as Allah Says (interpretation of meaning): {And We send down from the Qur'ân that which is a healing and a mercy to those who believe (in Islâmic Monotheism and act on it), …}[17:82].
As for Salat al-Hajah (prayer of need) it is permissible according to some scholars for the Hadith reported by Tirmizi, Ibn Majah with a weak chain that the Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever is in need of something from Allah or from someone else has to make Wudu, make it perfectly, and then perform two Rak’ah."
Know that one should not ask Allah for anything that contains a sin or a cutting of the kinship ties, etc.
Finally, we advise you to be steadfast on the way of Taqwa (piety) and thus you may protect yourselves from evil eye and bad effects. Also, we advise you to think good of your brother and other relatives and treat them kindly and pleasantly. This may develop into love and good relations amongst you and keep you away from Satan.
Allah knows best.