it sounds like a psychosomatic condition, which is where mental anguish causes physiological symptoms.
Severe stress and anxiety are known to cause many physical ilnesses/problems. it sounds like the videos are making you very anxious and your anxiety is causing your body to react this way.
you should explain your situation to a doctor or the school nurse, and they should be able to help you. sorry i don't know more - i only know what i've learnt in psychology myself.
but if you research "psychosomatic illnesses" on the internet it may help you to learn more about it. also talk to your Psych teacher - he/she should understand as this is relates to psychology. if it is really too traumatic, maybe you can be excused from watching the videos.
understand that this happens to alot of people and it's nothing to be ashamed of. i hope u find a way to sort this out!