If I'm understanding correctly, you don't want to see a trend, per se, you want to see all the tweets related to a specific topic. This is actually pretty easy to get in a format that will allow you to manipulate it into usable data.
Using queryfeed.net you can create an rss feed of any keyword you like. In your example, your favourite musician Justin Bieber. On queryfeed enter justinbieber.
That gives you an rss feed of
https://queryfeed.net/tw?q=justinbieber
Now that is just a raw feed that doesn't give you everything, it just gives you the most recent information. You then need to capture the data using a simple database and then you can build queries off the data.
Its probably better to use the official Twitter API but this could get you started.
Is this more what you were looking for? There is nothing "off the shelf" that I'm aware of. You'd have to build it.