How can I tell if a balsamic vinegar is good?
Well, it IS vinegar. However as you probably already know, higher quality balsamic vinegar is less sour and more rich tasting than its cheaper counterpart. It's unlikely that your balsamic is spoiled--in most ways vinegar is as spoiled as it's going to get.

More likely is that you've uncovered one of the issues with balsamic vinegar: Most of what you can get in a supermarket is of low quality, and is not produced in the traditional way (years of curing and evaporation in wooden casks). What you can get is more likely to be much more mundane wine vinegar with flavorings. And that is often more acidic-tasting and pungent than the real thing (which costs an arm and a leg).

I'd say sample it carefully and see if it's as sour as it smells. It might be OK, or you might want to find a new brand or get it at a store that goes through it faster (check the best by date, if there is one).