Re-querying an Agency

If you do requery, don't mention a previous query.

As to whether you should or not, check the agency's policies. Some say they don't like it. Some don't really comment. If they don't comment then you can try, but be aware that they might actually remember it. If it was just a query they rejected before, they might not remember at all, though. Then it might help to requery.

Also, some people say that you should change your title, but I don't see how that could really matter in the end...

Did they look at chapters or was it a standard 'dear author' rejection?
If it was the latter then it is pretty unlikely that they would remember you. The rejection was from last year's intern and they've moved on.

If you've done a major re-write (which it sounds like you did) then you are probably OK. Like Reenkam said, don't mention that it is a re-query. Renaming your book may also help. Some agents keep a database, so a new name could help you sneak through.