How can one overcome the feeling of guilt and fear of divine punishment after committing a major sin, especially when this feeling conflicts with the ability to focus on essential life matters such as studying?

Allah's forgiveness is greater than any sin, and sincere repentance erases sins. The one who repents from a sin is like one who has no sin. So, if you repent with sincere repentance, your sin will not harm you, neither in this world nor in the Hereafter.