You can become a project manager with no experience, provided one of the following conditions is met:
- Your father/sibling/close friend owns the company or you have some very close ties with the a senior in the company.
- There are less than 5 people in your company.
- Your company doesn't really care about project management
In all other cases, you do need to have experience in order to become a project manager. The very basic scheduling experience that you have is not enough, there is a process to learn and there is some real experience to be gained and learned. You can start gaining this experience by expressing your desire to become a project manager to your current project manager (make sure he or she doesn't feel threatened), and asking for small scheduling/management tasks. Sooner or later you will move up to a project coordinator, and later to a project manager.
You can also advance your career (in project management) much more if you have move to another company after spending a year as a project manager in your own company (to the second company, you are considered to be proven project manager and you will get more respect, and more money...)