Okay in short, I'd say take some time off and give your body a chance to recover, perhaps even a week or two? I can imagine you're itching to carry on with training and race preparation, but what if the shin splints develops into something more serious and sidelines you for part of your XC season? We both know you'd be gutted!

Do you want to know if you'd be able to run through it? The truth is this is a very difficult question to give a definitive answer to, and as you may fear the best answer anyone can give you is that "Only you really know how you feel", the best anyone on here can do is to give you advice on making that decision yourself.

Firstly I would indentify whether you are experiencing 'pain' or 'discomfort'. The two are pretty similar, but to me pain makes running very hard and makes your body wants to stop, whereas what I would call discomfort is something that makes you feel off your best and inconviniences you - making running less enjoyable.
If you're experiencing 'pain', I would not hesitate to say don't run another step and rest it until recovered, then ease yourself back into your training. If it's discomfort then you need to base your decision purely on how you feel - my personal experience is that if I feel shin splints coming on (I normally suffer in one leg too - I have a funny running gait i think!) then trying to run through it tends to make things worse and ends up with me having to take time off.

Try not to base your decision on your upcoming XC season start date; you have an injury and regardless of what upcoming events you have you need to make sure your body recovers properly.

If you're going to try and run through it, minimise the impact on your lower legs by running on softer terrain, try to avoid asphalt/concrete (and running tracks too if you currently use them), and also ease back a little on your training and give your body that little extra chance to recover.

Best of luck! :o)