Getting vaccinated - whether for Covid or flu or shingles or etc. and having a complication is not a "work related" injury, even if my employer arranged for a mobile unit from (name of health foundation) to do the vaccinations in a company parking lot. The VAERS database is maintained by the FDA, and doctors are the people who have the knowledge/expertise to report to it. There is no need for duplication.
If NFPA 2112 rated Flame Resistant clothing is required in my workplace, and when I put it on, I have a severe skin reaction to the flame retardants in the clothing, is that a work related injury?
Ordinarily, I wouldn't spend that sort of money on clothes, (triple or at least double the price of similar clothing that is not FR), so other than for the OSHA requirement that I wear it, I would not come into contact with it.
I would contend that severe reaction would be a work-related injury.
Same for the "side effects" of anything in or on your body
required by OSHA to have the job, and OSHA is the mechanism by which this mandate is being enforced..