Yes, colleges will read your entire app, including LoRs, in the context of the school you attend.
Do any of the colleges you are applying to require a counselor LoR? If not, that LoR and adding in a blurb about your hospitalization and impact on grades is a moot point.
If they do write an LoR and don’t put anything in there about your hospitalization, at least you will have the few sentences you wrote about it in the additional info section. That’s the best you will be able to do, and that is an appropriate use of that section.
Lastly, please ensure your application essays have proper punctuation and English spelling/grammar.