Marie, your experience with a frozen brake brings back memories of my similar experience with my then almost new (less than a year old) trailer. In my case, the adjuster assembly in the brake disintegrated and pieces of metal in the brake drum caused the brake to lock up (or make horrible noises) when backing up. Fortunately, it didn't seem to cause any problems when moving forward except to make a rattling sound.
I replaced that OEM brake with a new one from e-trailer and then, in the next year, the other side OEM brake failed the same way! I've replaced that brake too.
I have no idea what caused these failures, but the new brakes don't seem to have the same weaknesses.
Regarding your axle, I'm pretty sure you'll have to replace the whole unit. I think they run about $400, but I could be mistaken. I priced one back when I was thinking of trying to upgrade my axle to one with a higher weight limit, and that was about 7-8 years ago.
- Jack