Currently our team members report any impediments in the Daily Scrum Standup and the ScrumMaster takes ownership of them and gets them resolved. I would like to know whether we should track Impediments in the Agile PM tool just like User Stories and Defects/Bugs.
Who Owns Impediments
The Scrum Master should not be "taking ownership" of impediments. The role of the Scrum Master is to facilitate communications and referee the process; the whole Scrum team is responsible for addressing impediments.
Tracking Impediments as Sprint Backlog Items
With that said, impediments that can be solved with a hallway meeting or a phone conversation probably don't need to be tracked. However, if the impediment is significant enough to generate an in-sprint task, you should definitely create a user story and place it on the Sprint Backlog.
Note that in-sprint user stories shouldn't add story points to the sprint, since they should generally be dependent stories of some other Sprint/Product Backlog item. However, if an impediment outgrows its parent story, either in level-of-effort or scope, then it needs to be escalated to the Product Owner to see if: