The bad news is that if your body fat is 27.7%, you are indeed overweight, regardless of what your BMI states. It also means that you are carrying way less muscle mass than you should be.
The good news is you can easily do something about it with specific lifestyle changes. Unfortunately this doesn't mean vague things like promising yourself to eat healthier, jog to a shop further away from home, or walk up to your flat instead of taking the lift. You need to embark on a proper and above all consistent exercise and nutrition programme to make any significant change.
As Lynx said, it really doesn't matter how 'bad' your starting point is. For her, running 2 km was pretty pathetic. For you, it might be unimaginable. Big deal. Just start with something you can handle. If you keep at it, your fitness level will increase. (In my experience, cardiovascular fitness improves very fast when you keep on exercising regularly.)
I'd recommend beginning with 30 mins of fast walking at least 3 times a week. (NOT running - you clearly need to work up to that.) As a rough guide, you should be moving fast enough that you'd find it hard but not impossible to keep up a conversation. I personally find that it's best to do this in the morning. For one, it's cooler. For another, in the evening you'll be tired and it will be more tempting to find excuses to skip it "just for that day". With every week that passes, try to walk a greater distance in the same amount of time.
Next, you need to get cracking on a good strength building routine to build up your muscle mass. While you can Google bodyweight exercise routines that you can perform at home, it's still better to sign up with a gym and a personal trainer to show you the best exercises for your needs.
Along with cardiovascular fitness and muscle strength, you'll also need to work on flexibility. That's something a PT can take you through as part of your gym routine.
Finally there's the dietary component. That means cutting down on starchy carbs and upping the leafy carbs and (lean) protein you intake. Chicken and fish are the meats of choice. If you are a vegetarian, adequate protein consumption can be a problem however. (I'm afraid I don't have an answer to this one.)
Exercise - as opposed to sports - is arguably fairly boring. You can make it more interesting (and effective) by challenging yourself to do that bit better every week. As I mentioned with walking/running, you can try do go further in the same amount of time. With gym workouts I've found it very useful to keep a workout log where I note down the weights I use and the rep range. Every week I try to do that bit better - by either increasing the amount of reps with the same weight or, if I hit my target rep range the previous week, increasing the weight used. My workout log is essential to keep track of these numbers. It also acts as a great encouragement when you are feeling under motivated to compare where you are currently at to where you were a few months ago. (It also acts as a good kick up the arse when you've been slacking!)
Remember, the real key to achieve your goals is to be CONSISTENT.
"Both politicians and nappies need to be changed regularly, and for the same reasons."