How can I enter the U.S. after an extended stay outside the country due to medical conditions?

It appears that the reason why you could not return to the U.S. is acceptable. However, the presentation of your records at the border may not suffice as any of the officers at the border may not be able to discern your position. Therefore, there may be a need to seek a legal process prior to entry in order to be properly allowed to reenter as a result. Also, consider contacting the U.S. embassy or consulate in the country where you are before heading to the U.S. You may address your situation better with the consular officials.

If you have a valid green card, you do need to be ready to show that at the time you left you planned to return after a short visit, but that there were circumstances beyond your control that caused you to be abroad for longer than you anticipated.

You should apply for an SB-1, returning resident immigrant visa, at the U.S. embassy or consular office in your home country. Contact that office directly for instructions about how to apply. You will need to show your medical records and other documents at that time to prove you did not abandon your immigrant intention.

It is probably best to get a travel document from the consulate.

You will be admitted, but you could be put in removal proceedings. Bring proof of why you could not return to the U.S.