As correctly pointed out by @Anonymous Physicist, the “Common Rule” defines research as:
A systematic investigation, including research development, testing, and evaluation, designed to develop or contribute to generalizable knowledge.
Simply reading the “Common Rule” definition of research, it would seem that a case report would not qualify as “research” because it is non-systematic. If a case report is not research, then it would seem that it does not need to be reviewed by an Institutional Review Board (IRB).
But, like so much related to the requirement (or non-requirement) for review of particular activities by the IRB (or ethics board), policies about case reports in the United States are not uniform among institutions. And there are further regulatory wrinkles due to HIPAA and problems that may arise from journal policies.
Writing up and publishing a case report generally uses protected health information, that is information that permits an individual to be identified. Access to and use of this information is regulated by the Health Information and Portability Act (HIPAA) and, at the institutional level, decisions about access to and use of such information is overseen by a “privacy board” or a “privacy officer.” The IRB often, but not always, serves both as an ethics board and a privacy board.
An institution might not require IRB review of a case report but would require review by a privacy board or a privacy office (or the IRB acting as a privacy board).
Empiric Data from 2017
A 2007 JAMA publication reported on the policies with regard to review requirements for case reports at medical schools in the United States. 
Of 124 medical schools surveyed, 116 (94%) responded. The following results were reported:
“Ninety-one (78%) of the responding schools did not require IRB approval for a case report.”
“None of the 25 [that required IRB approval] required full IRB board review; 17 (68%) required IRB notification; and 8 (32%) did not have a fixed policy but considered whether the report should have full or expedited review on an individual basis. Six (24%) conducted reviews because they considered case reports to be research, 8 (32%) for privacy requirement, and 11 (44%) for both purposes.”
The Journal Problem
A further problem that can arise when attempting to publish about work that was not reviewed by an IRB is a requirement by a journal that the work being presented has been reviewed by an IRB (whether or not it was required to be reviewed) or a request by a journal for documentation from the IRB that the work was NOT required to be reviewed.
The advice by others to “ask your IRB” seems apt. The advice might be expanded a bit to suggest (given the additional complexities that arise because an author of the case report is also the patient whose information is being reported) that the OP ask their IRB to review the work formally and issue a formal approval of a plan to publish the information by those who will be authors/co-authors. This is the safest thing to do (although bureaucratic)
 Panda M, Heath GW, Desbiens NA, Moffitt B. Research Status of Case Reports for Medical School Institutional Review Boards. JAMA. 2007;298(11):1277-1278. doi:10.1001/jama.298.11.1277
https://jamanetwork.com/journals/jama/fullarticle/208845 Johns Hopkins University