Your eyes shouldn't stop you.
From a retired DoDMERB official: "I really don't know if this has been brought up before or not. If your sphere (the first set of numbers) is less then -6.00 for the sea services and -8.00 for USAFA/USMA then you have no problem. If the Cylinder (second set of numbers) is less than -3.00 for all services you are good. No need for a waiver then. And if the numbers you state are correct then you should have no problems in the next year or so in getting into one of the service academies or ROTC programs from a visual acuity/refractive error stand point." (via www.serviceacademyforums.com)
You REALLY should get into a sport! Another club or activity would be good too. Also, remember, the academy wants to see involvement and leadership in your activities. Your academics will help your chances greatly, especially if you get great ACT/SAT scores.