Yeah, the outdoor units are quite often not quiet. Which matters with houses on small plots very close to each other. For that reason a water-water (earth-water) heat pump would be preferable as that's much more quiet but also much more expensive.

My nose simply doesn't work with it, I get an allergy-like reaction that never stops (non-allergic rhinitis), and my wife has the same issue, and many people I know too.

Rhinitis is not exactly a disease. It's just a matter of your body getting used to it. Most likely it disturbs existing dust. Also - does your house have proper ventilation system? In high co2 environments I get rhinitis too.