So basically, it's belch constantly forever, or take a shower repeatedly until the smell fades.

This really hinges on the definition of continuously.

If taken literally then you are farting or belching at ALL TIMES. Thus I would pick farting, since belching would prevent you from talking.

On the other hand if it just means "all the time", like say once a minute, I would take belching, since its less gross.

I guess I'll assume it means it literally. That you are belching or farting at ALL TIMES.