If you were a typical member of the sedentary population, a Paleo-style diet could be sufficient. But you're not. You are an active, developing young athlete with a serious commitment to training, far from average. (See Caution: Low-Carb Diets Are Not for Athletes.)
You don't struggle to get to the gym. You practically live there. So between exercising at least four times a week, attending practice and playing games, your body demands carbs. I'm not bashing the Paleo diet. It's a great program for optimizing hormonal output, minimizing fat gains and preventing hypertension in inactive people.
For you as an athlete, however, performance is everything. And carbs must be a part of your arsenal. Feed your body what it craves for fuel during hard workouts, and watch how much you improve as a result.
Athlete's Carb Considerations
Carbs help fuel your training sessions, meaning you recover better, your muscles look fuller, and you sleep better (because carbs release serotonin). On active days, you should be taking in two grams of carbs per pound of body weight. For example a 180-pound male requires 360 grams of carbs per day, ideally split among six meals, around 60 grams per sitting, with up to 100 grams in the post-workout window following hard exercise. Protein is important too. You need a minimum of 1 gram per pound of body weight to rebuild and repair broken-down muscle tissue.
If you're an athlete with a less than optimal body fat percentage, you might want to limit your carb intake to one gram per pound of body weight. If you're in this category, you could stick to Paleo-style eating for meals that don't coincide with exercise. (See Building a Healthy Low-Carb Diet for Athletes.) For example, if you plan to work out at 5:00 p.m., you could eat Paleo meals for breakfast and lunch; drink a protein/carb shake before hitting the gym in the afternoon; and follow it up with a big meal of more protein and carbs after you're done, before reverting back to Paleo before bed.
For an opposing viewpoint, read Is the Paleo Diet Right for Athletes?