Long post, I write personally a lot and I've tried to describe GD before
I've thought about describing gender dysphoria before.
It's not so stereotypical a thing as "A woman trapped in a man's body" (Or the reverse), at least in my case, I've never felt trapped. But then again, maybe philosophical differences make my body inseparable from my mind.
Anyway, it's not a sense of entrapment, at least not entirely. It's not "as if you woke up and had that opposite genitalia", it's not akin to phantom limb. This is because such analogies note a change from something previous. If you woke up with the opposite parts, you'd still have lived much of your life with things set up correctly. It's a different sensation, a very deep seeded sense of something being incorrect.
Entirely hard to exactly describe. But a great sense that things do not match up. Not (as some might assume) a choice, very much if it was I would've chosen differently. But more similar to certain genetic diseases we are born with. But that again is not how it truly "feels". The dysphoria is perhaps comparable to the sensation one receives when they feel are disoriented. Although I think maybe one of the most accurate comparisons can be found in videogames.
Granted, this may be because they are such a large part of my life. In certain games, one may start playing them and have a sense that something is, not quite right. The frames may be slightly jittery, a touch too slow, the sensitivity of the mouse is too much or too little, the field of view is subtly off-putting, the shadows a little too dark, the UI clashes in a way not immediately apparent. It is a great collection of small things that gives an immediate sense of "something is not right here". Oftentimes this goes away with some adjustment of the game or simply growing used to it.
Now, take that initial feeling of disorientation and move it beyond a superficial experience. Take that disorientation not from a game that is beyond yourself, but from the very parts you use to interact with the world. The eyes you use to see everything, the hands you feel with, the voice you speak in, the body you will wash, the clothes you will wear, in nearly every waking moment take that which is for granted and twist it slightly, give everything the sense that "something is not right here". If I were to do this purposefully, your clothes fit too tightly, things are blurry in your vision at random intervals, your voice sounds queer but no one notices, your body feels entirely disgusting but no amount of soap is making it clean.
Yes, that is more accurate. That confusing anxiety when you understand that something is entirely wrong but it doesn't go away with time, it doesn't stop because you can't close the game, it sits with you and scratches at you. Some people ignore it for a long time, some people (such as myself) attempt to live a life as if they had no body, but I think at the end of it all, that feeling of an innate break of self becomes too much. The overwhelming sense of disgust becomes too great and all the walls we put up fall apart.
But I think that has become too poetic. It's hard to describe, this feeling. At the very least I can say that I don't like it, I can say that it drives me to suicide.