And nothing which could correlate with this has happened, so I don't understand why it feels so hard and different this time. Anyone gone through this kind of situation?

Do you mean by gagging as chocking, like your short on breath or your airway is being blocked?

I mean like almost throwing up. (retching might be the right word?) 

You know like a vomiting reflex?

It sounds like you are choking on your tongue. The tongue is reaching deep in the throat that it's initiating the throwing up reflex. 

That seems to be correct. Am I doing it wrong?

Posted by: Tester

That seems to be correct. Am I doing it wrong?

That's possible that your suctioning your tongue too much, but its also possible that you have very limited space in your palate forcing your tongue to do that.

I thought gagging was a common symptom of doing the posture correctly, since it's an unfamiliar position for the tongue to be in (if not used to it already) with not enough room to sit comfortably. Since doing a mild clench along with the tongue posture, I also feel that gagging reflex. I also feel anxiety when doing it, and it resurfaced half an hour later when not even doing the posture. Has anyone else had that at the beginning of retraining their tongue?

If I have a limited space does that mean I need a surgery or can I make it larger by mewing?

If you had perfectly optimal room for your tongue to begin with, it's unlikely you would be concerned about your looks at all, so no, you don't need surgery unless you have a severely narrow palate width or something. Mewing should be able make more room, that is the whole idea of it. 

Without additional information like arch shape and width, etc no body can tell you but surgery is something to discuss with highly qualified doctors first.