I had this issue in Sims 2 while using custom content, so it looks like that could the problem.
In Sims 2 at least, what happened to me was that the game couldn't display some (bad quality) custom clothes that my Sim was wearing, so it just disappeared. Did you install clothes, hair, eyes, makeup or something like that and used them in this sim? Sometimes you're missing a mesh and that's why the game can't display the stuff correctly.
Also, I didn't quite understand (sorry, I'm not english-native
. Can you still control the Sim or is it stuck? If you still can, you could try sending the sim to a mirror or a wardrobe and change its clothes/hair/makeup whatever for non-custom content and see if it gets fixed. It worked for me in Sims 2 but I don't use any custom content in Sims 3 anymore so I couldn't say if it's the same.
I would recommend the same as Pam said, starting the game without custom content and see if it works again. If it does, it means you have some bad custom content in there. You can either remove all of it permanently (which would be my advice, but I know you may not want to) or just remove all of it and put it back in small groups at a time, load the game and see what happens. That way you will determine which group of items is causing the problem and will be able to delete the bad custom content.
