Apply for an extension of your visa IMMEDIATELY explaining that it is for medical treatment. Include a letter or records from your doctor with the application.
Well, if you are a couple of days late to leave the country, it won't legally hurt you. But if you plan to stay for a long time/you don't know how long, then you should apply to extend your status. Also, make sure you keep copies of medical records, and ask your doctor to write a letter explaining the need to stay in the country. Good luck!
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