Okay, first of all, despite what they said at the pet store, Bettafix actually isn't good for bettas. It contains tea tree oil which can harm a betta's labyrinth organ, which they use to breathe from the surface.
Secondly, how long ago were the tetras and other fish introduced? It's always a good idea to quarantine new fish for at least a week to wait and see if they develop any illnesses.
Okay, treatment. Looks like Nuggest has some fin rot all right and he's a bit bloated (did he just kill the tetras or did he eat a bit of them too? I know, very gross question, sorry about that). I'm worried he has a bacterial infection going on but I don't think he caught it from the tetras. He looks a little bloated in the "before" pics too. How long was he in his betta cube and how often did you change the water while he was in there? I am concerned that he caught his bacterial infection from poor water quality while in the betta cube. :/
I would suggest floating him in a small container in the 10g to keep him warm (I assume the 10g is heated). In the meanwhile, if it's possible, you may want to run to the pet store and see if they have these two things: Jungle Labs Anti-Bacterial Medicated Pellets and API General Cure. If Nugget will eat, start him on the pellets. If he won't, start him on the General Cure.
For his breathing, you may want to lower the water level in his container to just about an inch so he can easily reach the surface to breathe. Make sure the water he is in is kept as clean as possible. Do you use water conditioner when you do water changes? If so, what kind? Does it detoxify heavy metals? If not, use API Stress Coat as your water conditioner.
I'm sorry I can't offer much more advice. I just hope we're not too late. :( Hang in there, Nugget!