In general that’s absolutely true, but the comment by @Phen0mejon you’re replying to does give a context where …already not… can make sense (and doesn’t mean the same as …not … yet… would). But as @Theron126 says, the Russian sentence is saying a simpler thing that doesn’t need such a contrived context, and already not is an over-literal translation for it.
Russian words for going are split into many pieces:
иду means walking in one direction.
еду means taking transport in one direction.
хожу means walking in various directions.
езжу means taking transport in various directions.
So from the context, хожу is the correct choice.