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I'm sorry if this is inappropriate but what health reasons prevent you from getting vaccinated?
There are allergies to vaccines (not to the dose, but to everything else that is in the concoction that enables it to work). Also, immunocompromised people often can't take vaccines. Usually you can get a doctor's note explaining this, and you can participate in daily life normally (like going to school or college, which rightfully require vaccinations). I don't know if policy around the COVID vaccine is different...…
There are multiple vaccine formulations available, and they largely do not overlap in terms of potential allergy triggers. If you're allergic to a component of the mRNA vaccines, that does not preclude you from taking an adenovirus vaccine, or vice versa. https://www.cdc.gov/coronavirus/2019-ncov/vaccines/recommend...