To be really sure you would you need to go to the immigration, there you get another 30 days . That might not be enough ? You can complete the papers online and print . Make sure you have two photos ( recent ) . You still need to do that the agent will ask you for it . But even the agent is not a guarantee that you not need to go there . Some immigration still ask you to be present . USA doctor I doubt they can help . The documents would have to be translation most Likely and Stamped by US consular or embassy . So better get those information . Some hospitals help with an extension for visa for a fee , you should ask . Hope you get better soon
Do you come into Thailand with a visa exempt or an any visa ? The airline will ask you to show an onward or return flight after you 60 days exemption visa . They not allowed to take passenger they are liable to check on this . If you have an retirement visa or any other you not need a return / onward tiket