Sounds exactly like my DD, who does faint (helping dress the Thanksgiving turkey, school field trip to "hospital-land," etc.). We also had a lot of trouble with eye drops and vaccinations. The word blood or hearing about anything related to the circulatory system were extremely difficult for her. She also has an aunt with similar issues.
It's actually fairly common. I did let her teachers know, and they were all very understanding, some letting her be excused for the class, some offering alternate material, etc.
Over time, the problem has eased somewhat; she is still bothered by the topics, but the words (and vaccines/eye drops) are not an issue any more. She enjoyed middle school health and biology without problems. She can usually control her response, and is tuned in to the pre-syncopal feelings so she can prevent outright fainting- she's gone a few years now without an event, so there is hope, though I doubt DD will ever choose to study medicine😊.