Can you naturally 'grow out of' ptsd?

Not really. Ptsd is a serious debilitating disorder that should be treated. It will sometimes leave you emotionally scarred permanently. There are neurobiological changes that take place that you may never "naturally grow out of ".
PTSD gets hard-wired. I believe that in some cases of mild ptsd, talking with relatives or friends who are supportive and empathic may with the tincture of time be sufficient to move past the ptsd. However, i very much agree with the other physicians who provided precautionary responses. Ptsd can become progressively more hard wired into the brain with time. It becomes more recalcitrant to treatment. Get help.
Management. Typically with the more severe cases of PTSD, the medical/psychological is not so much about curing it, as it is about effectively managing it. It never goes away in the sense of being cured. In a way both patients and doctors are students of managing severe cases of PTSD, and never master of controlling it, unfortunately.
PTSD. No. Left untreated, it will worsen and, in some cases, lead to very serious consequences, such as depression and suicide.