Really good to have Project management as a career. As you have taken project management courses and taken CAPM also it is good and will surely help to move up to PM fast. It also matters from where you have taken the course, they will also help you. Also, you have good experience with good companies.
Now you have learned the Project Management process, along with your certification and working with management companies all you need is to move up the ladder with some real experience. All that I would recommend is to work in close co-ordination with keen interest to learn the skill from your PMs in your company; wish they will help you. You can convince PM in your company to train you and give you change to train and also become PM, let them know that you can Also, do latest PM certification so that you get more opening. Project management career is very challenging and
Project managers are there to plan and manage the work, a project manager needs to posses general management skills and also knack for solving problem. Project Management is all about meeting deadlines, analysis, taking quick action and being responsive, excellent communication skill. Projects are managed and also priority is set, these all activities are organization’s portfolio of work and share requirements such as alignment with organizational objectives and the effective allocation of resources.
Be a leader and a manager, team builder, problem solver, influencer, good organizer, excellent communicator, set up and manage budgets and competent and consistent planner.
Project manager can make a lot difference in organization as a PM works under a set of requirements and objectives. So if you posses all the above skills, it will become very easy for you to become a PM. Few links that may be of great help:
http://www.apm5dimensions.com/blog/what-turns-normal-human-being-project-manager
http://vacancies-jobs.net/description/how-do-you-get-a-job-as-project-manager-with-zero-experience
Also, you can search in Google "become project manager with zero experience" and you can find more detail answer to your question.