Severine, it's
completely do-able. Hal Higdon's training programs are great...and
he's a ski writer, to boot! Another alternative, which can be tailored to you, specifically, is Smartcoach on Runnersworld.com.
Pull the trigger, register, and that will motivate you to be diligent in the training. I think the toughest part of what you're aiming to accomplish is that you'll likely have to do much of your training indoors. With respect to the running 3x a week thing, my opinion is that it's not the number runs per week that affects likelihood of injuries, but rather, the increase in mileage. Like tcarey wrote, the common rule is to increase weekly mileage by no more than 10%, and there's also usually a drop back week every 4(?) weeks or so. So, in my opinion, if it turns out that your Wednesday run is supposed to be 4 miles, but you're only allowed 30 minutes on the treadmill on the gym and are running 10 minute miles, then find a way to work that mile into another workout that week. I think most beginner 10K-ish programs have the "maintenance" distances somewhere from 2-4 miles. I don't think moving a mile from the 4 mile workout to a 2 mile workout is a huge deal when one's goal for a particular race is to complete it.
Also, another thing to keep in mind is that treadmills tend to be a softer surface to run on than asphalt, so there may be an adjustment period as you move from indoors to outdoors. Since it sounds like you had knee issues in the past, this is just something to take note of.
Are you doing a 5K to wrap up the 5K training? I would recommend it if you aren't already planning on it. Then, somewhere in the middle of the 6.55 training, I'd do another 5K so you can see how much you've improved - that's usually a huge motivator. It'll also provide a guage for how you may do in the 6.55. A really interesting tool to estimate your potential is the
McMillan calculator.
FWIW, I was so excited after running my first 5K that I immediately signed up for a 10K. About an hour later, when the adrenaline wore off, I was like, holy crap, I have to run twice that distance, how am I ever going to do that? We've all been in your shoes at some point...good luck!