Just to back up what others have said... weight will play a big part in your success and take huge amounts of stress off your shins.
Also... don't practice the bleep test again more than once every couple of months over the next 6 months.
Couch to 5K is a great way to go about it. If your shins are really hurting though, read all about shin splints - which are very common in people starting running - and which can soon become a stress fracture if you try to plough through it without care.
9 months is both a long time and a short time! 9 months is plenty of time for you to achieve this (and frankly, if you do not, then you may not be ready for the discipline of the force - unless there is a very strong reason why you don't succeed... like a long time out through injury). But 9 months will soon go... so be disciplined from the off.. but that doesn't mean go racing off too fast. Steady away will get you there.
With 13 weeks to go, changing plans to another one aimed at your current running ability (but perhaps a little more intensive) would be no problem. But there really is no need to panic. You could also choose to stick with the current plan, but throw in an extra run for as many of the remaining weeks as possible... even if it's a 3-6 mile recovery pace run, it will make a big difference. It's that latter route that I'd recommend... but if you can also "lose those pounds" at a steady, sustainable weight, then that will make a great difference too.
But you are just having a crisis of confidence (common, but in your case, unnecessary)... because the times you're running are great. Surely you can see that a 2:22 half marathon, 15 weeks from race day, shows great promise. And 2:38 in a half that includes 6 miles on a sandy beach... likewise.