It might be a really big poop, I don't think it would be an organ if he is still alive.
What is your set up? Size tank, temperature, your water change routine, feeding schedule etc. the more information the more we can help :]
My betta would dart around his tank whenever I walked passed him the first few days. He would bang into the walls of the tank and everything, worried me, but now he doesn't do it anymore, I guess he was just very jumpy at first. But if he is glass surfing too he might be trying to scratch himself, which would be a sign that he has an external fungus or parasite that is making him itchy.
I suggest keeping his water around 77 degrees, and do 100% water changes everyday for about 2 weeks. If you can see any other external abnormalities, and can identify it as a fungus or a parasite (googling, or posting a picture to us) you may want to start treatment of some sort, which I'm sure someone else can help you with here :]