Get a lawyer.
You should provide proof that your medical records can not be transferred to your doctor back home.
Plus, immigration will be very interested in knowing who is paying for all the medical services you are receiving in the US.
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You can even fly to space yourself if you have the equipment, training and funds. There is no medical parole from inside the country. The form is I-131.
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Humanitarian parole is filed using i 131 form. However, you are already here, and it will be solely up to the DHS if you can stay longer. You can try doing it yourself; a lawyer is highly recommended.
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