Shame - why, who cares? In fact most people will hardly notice you - it is myth to think that people take a lot of notice of random others - we are just 'wallpaper' in their lives.

Perhaps your health problems weigh heavy on you and and this transfers into other situations and anxieties?

As for the exam, speak to the invigilator - they will seat you near the exit I expect, so you can leave/return without causing disruption or drawing attention to yourself. Or better get a note from your doctor and present this to the authorities - they must encounter may such problems and will know what to do.

Even if this is understandable insecurity and anxiety about your studies and health, you still might need help - does your university have a Counsellor?