The value of proper nutrition towards fitness cannot be understated, it is it's cornerstone. Apart from other things, it prevents/lessens ailments (heart disease, obesity and even cancer). So to attempt at being fit, toning muscles and so forth without a good diet regimen is an entirely useless act.
In order to target your biceps alone you have to do exercises which emphasize them only. While correctly working different muscle groups, one does not re-engage their biceps-- you are merely confusing full arm movement as being equal to bicep-exercise. A muscle group is emphasized by repetitious contraction and expansion of it, albeit under continuous stress, which reasons the use of weights to imitate it. The inclusion of added the stress sets it apart from normal circumstances where it would be absent and the muscle is 'compelled' to develop to counter the stress. When you work different muscle groups, you isolate this stress to them alone and which is why other muscle groups aren't re-done or over-done. I could tell you some specific exercises which target your biceps alone.
It's good that you're active in other sports. Weighted-workouts are generally meant to build/shape muscle tissue/ fibers, where it is active sports that cater more for stamina, endurance and flexibility. Speaking of sports, I would suggest the game of Squash to you, which is widely considered as probably the most health-geared sport. It works both the upper and lower portions, increases stamina and gives one a complete cardiovascular workout, considerably much more than other sports. In playing say, an hour and a half of Squash, one easily burns about 1600 calories.