Should I fly to Laos to get a visa or go straight to Thailand for my medical procedure?

I wouldn't make any plans that revolve around getting a medical extension. The only assured time you can get will be the 60 days + 30 day extension. Medical extensions are not for recovery, they are for people that cannot fly. (As in you are admitted to the hospital and cannot even go to immigration to apply for the extension so the hospital has to do it for you)

𝗚𝗼𝗶𝗻𝗴 𝘁𝗼 𝘁𝗵𝗲 𝗲𝗺𝗯𝗮𝘀𝘀𝘆 𝗶𝗻 𝗺𝘆 𝗵𝗼𝗺𝗲 𝗰𝗼𝘂𝗻𝘁𝗿𝘆 𝗶𝘀 𝗸𝗶𝗻𝗱𝗮 𝗰𝗼𝗺𝗽𝗹𝗶𝗰𝗮𝘁𝗲𝗱,

you're a bit mixed up about visa issuing 😕

ALL thai consulates in the world are online eVisa thru the web-portal, there is no 'go to an embassy', You apply online, you upload your documents, pay, they email you the visa if it's approved in a PDF file that you print and show with your passport when you stamp in



If it's only 3-4 months, you could certainly fly in free stamp for 60 days (visa exempt) take the one 30 day extension for 1900baht, then check with your immigration office if you can do the "visit thai family 60 day extension (if you're married to a thai) OR get the documents from the hospital and apply for a medical extension (which can be granted from 30-90 days depending on immigrations)

Another option is;

If you're married to a thai you could apply online for a 90 day Non-O visa based on marriage thru the thai consulate in your country before you come here, that would get you stamped in for 90 days when you arrive and then you could take the 60 day visit thai family extension after that