Things wrong with just this sentence:
- You are responsible for learning material you missed - you are lucky they let you join the course late. Unless the course staff told you that you are not responsible for old material covered before you joined the class (which is unlikely, and quite frankly, unheard of), you do not have a case.
- You are responsible for knowing the information on the syllabus or slides, whether or not the professor goes over them in class. if the professor passed out the syllabus/information physically during class, but did not make them available later on the course website/Canvas, then you may have a case (although this is unlikely, since every professor I know makes sure that course information/syllabus documents are easily accessible online).
- The "you can miss this many classes without penalty" policy that many attendance-based classes at Michigan follow typically include sick absences as counting against the allowed allowance. These policies are NOT in place with the intention for students to use them as vacation days. If you have recurring/chronic health issues, you need to work with the professor and SSD to have the appropriate accommodations made. If the appropriate accommodations were not made despite you requesting them, then you may have a case.
- Does your email from your GSI just say that your absences were excused (which could be interpreted to mean that your allowance covers them), or does it imply that your absences would not count against your allowance? If the latter, you may have a case.
If you have a case, then feel free to reach out to the prof again clearly explaining the reasoning. If that does not work, the department chair and Ombuds Office are likely your best bets.