Your dream reflects a deep emotional landscape that intertwines your current stressors, particularly surrounding the JEE exam, with feelings of frustration and anxiety associated with your schooling experience. Let's break down the key elements of your dream:

1. Setting in School: The school symbolizes a foundational place of learning and your past experiences. Dreaming of your school suggests that you are processing feelings related to your academic journey, possibly feelings of nostalgia or anxiety connected to exams and expectations.
2. JEE Exam at School: The juxtaposition of the JEE exam being held at your school rather than the usual centers indicates a sense of being trapped in a familiar yet stressful environment. It may reflect your worries about the exam process and your desire for it to be orderly and fair.
3. Changing Exam Rooms: This part of the dream highlights feelings of disruption and lack of control. The shift in exam rooms could symbolize your fear of unexpected changes and the anxiety that comes from logistical issues that could affect your performance.
4. Frustration with the Invigilator: The invigilator representing someone you associate with rote learning could reflect your inner conflict about educational systems that prioritize memorization over understanding. Her slow response may symbolize your frustrations with bureaucratic inefficiency and how it impacts your academic performance.
5. Loss of Exam Paper: This represents a significant fear of failure or loss of opportunity. The feeling of anger and helplessness when your paper is taken away underscores your anxiety about not being able to perform to the best of your abilities due to external factors.
6. Shirtlessness and Embarrassment: The act of taking off your shirt could symbolize vulnerability and exposure. It may suggest feelings of being unprepared or not being able to present your best self in high-pressure situations. The transformation of your shirt into a modified uniform could indicate a struggle with identity and expectations placed upon you by your school or society.
7. Walking in Rage: This imagery reflects your emotional turmoil and frustration with your current situation. It’s a manifestation of your internal struggle, feeling that you are not being supported in your goals, particularly the upcoming JEE attempt.
8. Headmaster’s Interaction: The headmaster mistaking your situation for a birthday celebration could symbolize the disconnect between your internal frustrations and the perceptions of others. It may reveal your desire for recognition and support, yet feeling misunderstood or overlooked.
9. Cultural Event vs. JEE: This contrast highlights the feeling of neglect regarding your JEE preparations. It suggests a sense of alienation from the systems that should support your goals, emphasizing a perceived lack of focus on what is important to you in this moment.

Overall, your dream encapsulates the intense pressure you feel regarding your JEE exam, compounded by your current flu and fever, which likely heightened your emotional state. It suggests that you are grappling with feelings of inadequacy, frustration with educational systems, and the fear of failure.

Advice: To cope with these feelings, consider addressing your academic pressures by establishing a clear study plan for the upcoming exam. Make time for self-care, especially while you're unwell, and discuss your feelings with someone you trust, whether it's a friend, family member, or counselor. Remember that it’s okay to feel anxious about exams, and finding healthy outlets for that stress can help you regain a sense of control.