How to track social media mentions?

We are trying to use social media to gather feedback (good and bad) and listen more to our users/students (I work at a school.)

Is there any free/paid tool that allows us to gather all feedback (whether it be related to search terms or what) and let us get reports on it? Here are the ideal social medias.

Twitter
Facebook
YikYak (only available as app)
??? (Am I missing any big ones that kids use these days?)

I’ve Googled for some but there are just so many tools and I’d at LEAST like a free trial if there is a paid one that does everything we want. YikYak is a big one with the students over here so I’d REALLY want capability of tracking that.