There are many distinct aspects to project management, but focusing on the 'management' aspect, there are two clear sets of competencies that I would want to consider. One focuses on managing the process and the technical aspects of the project, and the other is associated with managing the people. These are not mutually exclusive - far from it - but the emphasis placed on each will vary according to the way that your organisation is set up to run projects.
If the PM is also a line manager, the ability to work with staff in a long-term relationship is vital. The skills required to do this are quite different from those of a PM who pulls in staff in a 'matrix' structure, with a separate manager looking after the long term needs of the staff. I suggest that you identify which model your company uses, and see how your skills map against the needs of the role.
Finally, if you are happy working with uncertainty and are able to see the big picture despite short term 'noise', you may be well on the way to being suited for project management. Don't expect instant gratification or constant positive feedback, but if you can thrive in an environment where there are high demands on your time, constant interruptions, and new challenges on a daily basis, while being able to stay in control and keep your people motivated, you are well on the way to being a practical and successful project manager.