I can't say how long it'll take you to get up to 15 minutes, but I can share my experiences with it:
Years ago when I first started jogging I did pretty much what you are describing, but I didn't watch a clock or anything. I would set myself little goals, like: "Try to jog to that light pole" or "Just jog to that driveway over there" and I would walk the rest of the time.
I increased my jogging distances gradually until one day I was jogging my entire 3.5 mile route in about 30-35 minutes. I did it at my own pace, always being sure not to push myself too hard/too fast and risk injuring or discouraging myself. It took a few months to get to that point.
Last year I started jogging again after several years of being inactive. I started off jogging at a VERY slow pace (hardly more than fast walking) for 20 minutes. I worked my way up to 40 minutes at a faster pace. Again, this took a few months.
Then starting around Thanksgiving I slacked off for a few months, and just started jogging again one month ago. As before, I am taking things slowly: I only jog for 20 minutes at a very,
very slow pace. I am not pushing myself too hard to do too much just yet. I will add 5 minutes in a few weeks, and so on and so on until I am back up to 40 minutes. As my stamina improves and my weight drops (again!) I know my speed will naturally increase.
So, through my experience the advice I would give is this: take things slowly and set small goals that you can gradually increase with time. Remember: do only what YOU can do, and don't compare yourself to anyone else. You aren't in a race or anything, so how fast you go or how quickly you improve isn't as important as just getting out there and moving your body!
Also, one more piece of advice: running/jogging is just as much a mental exercise as it is physical. What this means is that our brains will try very hard to talk us out of what we are doing! This is especially true when you are starting out, since you are taking yourself -- brain included! -- out of your comfort zone.
You have to find a way to ignore those negative thoughts (like "I can't do this!"), and push through it. Your brain will be very insistent and work hard to convince you that you are "dying" or that you can't do it -- but don't listen! I have found that I am ALWAYS capable of doing much more than my wimpy little brain is telling me I can when I am pushed into it.
So, don't push yourself too hard, but don't believe all those negative things your brain is telling you either.
its tought for me to run...
yet, so if I'm wrong, sorry, but a 10 minute mile pace is pretty fast for a beginner. Go slow. Try a 12 minute mile (5 mph) or even slower. 
I'd love to run a 10 minute mile but I'm slowly building my running ability. Just give it time and you'll get there.
Cake!!!
