All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We are not aware of any evidence that there is a particular Chapter that is recited to repel sorrows and anxieties, but this can be achieved by pondering on any Chapter of the Quran; Allaah Says (what means): { Those who have believed and whose hearts are assured by the remembrance of Allaah. Unquestionably, by the remembrance of Allaah hearts are assured.}[Quran 13:28] The Quran is the best method of mentioning Allaah.
In addition to the recitation of the Quran, we advise you, dear sister, to do the following:
1- Performing good deeds as much as possible as this is one of the reasons of living a quiet life and having peace of mind, Allaah Says (what means): {Whoever does righteousness, whether male or female, while he is a believer— We will surely cause him to live a good life, and We will surely give them their reward [in the Hereafter] according to the best of what they used to do.}[Quran 16:97]
2- Relying on Allaah and having trust in Him and setting the Hereafter as one’s prime purpose and concern. The Prophet said: ‘‘Whoever sets his entire objectives as one objective, which is the Hereafter, then Allaah will suffice him from the worry of his worldly life, and whoever is immersed in worldly affairs, then Allaah does not care in which valley this person is destroyed.’’ [Ibn Maajah]
3- Keeping company with righteous and pious women; as your seeing a believer and sitting with her reminds you of Allaah; it is for this reason that the Prophet said: "Do not befriend except a believer and do not share your food except with a pious person." [At-Tirmithi]
For more benefit on the supplications and mention of Allaah about sorrow and anxiety, please refer to Fatwa 86204.
Allaah Knows best.