shin splints are really a non-specific term...IF there area you are referring to is the front of your shin, specifically it is called medial tibial stress syndrome (MTSS)...the anterior tibialis muscle attached there, and you either get a tendonitis type picuture, or just enough swelling in the muscle tissue (from overexertion, or not letting the muscle recover, or repetitive stress...i.e. running)....it also could be a stress fracture from the stress on the muscle tearing away (microscopically) at the attachment to the bone.
The most common is a tendonitis / sweeling of the muscle in what is called the "anterior compartment" of you lower leg....there are four compartments....dividing the muscles with connective tissue.
Anyway, here's the skinny....you likely need new shoes...if you tend to wear down the outside edge of you shoes faster than the inside edge (look at all your shoes from behind, you'll see)...then you need to get some shoes that don't 'overcorrect' that...go to a local running shop where the guys know what they are talking about and can get you the right shoe.
Nike, I think it was, came out with shoes specific for pronators(described as above), supinators, and those who walk flat on their feet. Not sure if they still make them that way or not. If you tend to walk on the outside edge of you foot, and the shoes forces you to run/walk more flat footed, it stretches that muscle and tendon too much and you get 'shin splints'.
Anyway, this post has gotten way too long.....rest, anti-inflammatories will be key for a while....sometimes you are better in a few days if you get the right shoe, other times we are talking months. I used to do triathlons, got some new shoes, and developed 'shin splints'....cut down my distance to only 2 miles/day.....had to take days off....anyway, once I figured out what it was, I got the right shoes, had to change brands....took off a week, and was back up to running 5-8 miles/day. Never had that problem again.
Get the right shoes. Go to a running store where they watch how you walk barefoot and match you to a brand of shoe. Not sure what to tell you about game day vs practice...not sure if you guys have to wear a certain shoe.
sorry this was so long, hope it helps. Another alternative is to have inserts made for your feet with high arch support to put in your shoes so your stance is not overcorrected.