whichwho happened to be suffering from the same upper respiratory infection as Ime."
Those are great questions Guilherme. For your question about I versus me, see Oxford's discussion of personal pronouns.
"Many others" could be used if you delete "patients," but I like your current wording ("many other patients") better because it is more specific.
Note that including or omitting the comma before the word who slightly changes the meaning of the following clause. That is, if there are 10 other patients, did you (a) observe them all and they all had a related condition or (b) observe many but not all of those 10 patients, and all of the observed patients had a related condition? If the latter, which I assume is the case, the sentence is correct as it stands (i.e., without a comma before who).
I have a related video tutorial on this issue (it is really on that vs. which, along with changes in meaning, but the lesson essentially applies to the use of who as well.
Please note that I tend to work in U.S. English and specifically with academic writing, both of which favor a more precise distinction between that and which. I have been told and have read that British English is more lenient with the distinction, and in informal writing the distinction is usually less important.
Regardless, in your case above, including or omitting the comma before who does affect the meaning slightly, so it is at least a good exercise to think about (again, it is most likely that your current usage is correct). Hope that helps! :)