Maegan, what you may not realize is that you have an awesome opportunity right in the billing office where you are working! Coding and billing go hand in hand,so I'd encourage you to approach your supervisor, let him/her know about your coding interests and ask about projects or duties that you can do that will utilize your coding skills. Although some organizations have separate coding departments, I will tell you (as a coding manager) that my best coders have worked as billers.
The days of sitting at a desk, pulling CPT codes from the books and typing charges into the system are largely gone, because of electronic health records and computer assisted coding, so today's coders have to be knowledgable in all areas of the revenue cycle. That's one of the reasons that coders tend to need to be very experienced these days....there aren't many entry-level jobs available, as I'm sure you've realized.
Not only that---but you're employed in healthcare, in a related field where you're going to gain experience to move you towards a coding/auditing position. I'm willing to bet there area several thousand CPC-As that would give their right arm to be where you are right now. Take advantage of the opportunity that is right in your lap. Make yourself the most valuable employee that they have---be the person who is the problem-solver, the go-to person and the most reliable worker in the group. This work ethic is equally as important as are specific skills. If you show that you're a fabulous employee, opportunities will come your way. Good luck.