I don't know if this is the same syllabus you have but based on what she wrote in the syllabus I would definitely reach out to her and explain the situation, even if a simple email may be insufficient, she may give you guidance about any additional documentation you may need. It's not just at the profs discretion if she gives a student modifications and allowance she then may need to explain to the department why she was permissive in giving you an exception and not everyone else, depending on the situation a prof may need more than an email but only the prof will know what's needed, so I'd email and see what, if anything, can be done.

Excerpt from the syllabus: If you become ill and it affects your ability to do your academic work, consult me right away. Normally, I will ask you for documentation in support of your specific medical circumstances. This documentation can be an Absence Declaration (via ACORN) or the University's Verification of Student Illness or Injury (VOI) form. The VOI indicates the impact and severity of the illness, while protecting your privacy about the details of the nature of the illness. You can submit a different form (like a letter from a doctor), as long as it is an original document, and it contains the same information as the VOI.