An x-ray cannot detect smoke, especially to a light smoker like you. However, the effects of smoking are diagnosed via x-ray, including emphysema and lung cancer. But there is a different case for heavy smokers, as the x ray result shows changes in the interstitial markings referred to as dirty lungs.
We can't tell if it will show in your X-rays. But we all know that smoking has its negative effects in the body and the lungs is the part that usually gets affected more when we smoke. Hopefully it doesn't harm yours since you said you're just smoking occasionally. But if you really want to get better, you will never go back to that bad habit of smoking again. You can consider e-cig as a better and healthier alternative to smoking instead.
No I don't have congestion in my lungs neither I have any cough but my main concern is that do x rays show the carbon in lungs.
You haven't been smoking long so I doubt if you've built up congestion in your lungs. Do you have a smoker's cough? If you do then it may show up...but unlikely.
I want to give you a little advice. Quit now...just quit while you still can. I started when I was 17....and here I am at 55 desperately needing to get off of them...but one addiction at a time.
Do they look for smoking in the Navy? Sorry I'm kind of ignorant on this issue. When my father was in the forces everyone smoked everywhere including in hospitals.