Is resorting to the remembrance of Allah (dhikr) and reading the Quran when feeling distressed or psychologically tired considered an offense to them, given that this is taking them as a psychological cure?

It is prescribed for a Muslim, during times of hardship, to resort to the remembrance of Allah, the recitation of the Quran, and prayer. This is a commendable act, for whenever the Prophet (peace be upon him) was distressed by a matter, he would pray and turn to remembrance (dhikr) and supplication (du'a). Among these supplications is the du'a for distress: "There is no god but Allah, the Forbearing, the Great. There is no god but Allah, the Lord of the Generous Throne. There is no god but Allah, the Lord of the Mighty Throne. There is no god but Allah, the Lord of the heavens, and the Lord of the earth, and the Lord of the Generous Throne." He (peace be upon him) would also recite the two refuge-seeking surahs (al-Mu'awwidhatayn) and blow on himself when ill.

He taught his companions to resort to the remembrance of Allah during distress by saying: "There is no god but Allah, the Generous, the Forbearing. Glorified be Allah and blessed be Allah, the Lord of the Mighty Throne. And praise be to Allah, the Lord of the worlds." And for worry and sorrow, the supplication is: "O Allah, I am Your slave, the son of Your male slave, and the son of Your female slave. My forelock is in Your hand. Your command over me is past, and Your decree concerning me is just. I ask You by every name belonging to You which You have named Yourself with, or taught to anyone of Your creation, or revealed in Your Book, or kept to Yourself in the knowledge of the unseen with You, that You make the Quran the spring of my heart, the light of my chest, the remover of my sorrow, and the dispeller of my worries."