What you want to do with the rest of your career is really up to you. Project Management can be very rewarding. Project Management represents a stepping stone to management for many technical people. Having technical expertise will also improve your ability to manage without authority, an essential skill for any project manager.
Project Managment will involve much more than tracking and scheduling. In fact, good project managers build experience in all 9 knowledge areas and the 5 major processes of project management as specified by the PMBOK Guide. This means you will need to deal with people issues, budgets, risk management, and much more.
Shadowing the project manager is a good first step. Now you should plan on some formal training or education, and be sure to express an interest as part of your company's annual review process.