@DznyGrlSD, kudos on your journey to be healthier... and become a "serious" runner. *thumbs up*
Yup, you've got to start somewhere. And a couch to 5k training program is the best start. However, I would not recommend that you make a half marathon your first major race. Start with a 5k, any 5k, but one you will be comfortable running in terms of season (not in August) and terrain. Flat roads are better than hills for a first timer. Although concrete is killer on your knees, but most road races will be either concrete or asphalt. Training for a half marathon is around 19-20 weeks for a beginner.
If you're already using the TM 3-4 times a week, you're working on that cardio and more importantly for running distances, endurance. And use that TM for your training. To mimic the effect of running outdoors (wind), increase the incline on the TM to 1%. But do this after you've done a nice warm up few minutes.
Many training programs for first timers talk about Run Walk Run routine. Usually start with 30 seconds running, then 30 seconds walking then 30 seconds running. As you improve your endurance, you increase the run/walk/run times. Don't sweat (no pun intended) if you spend most of your training time walking for the first month or so. The point is to increase your endurance which will result in longer periods running at a faster pace. I would start with no more than 30 total minutes each training day with as many R/W/R periods you can safely handle. If you don't have a fitness tracker that includes a heart rate monitor, you might want to get one. Not only will you be able to track pace, distance, etc., you will be able to check your heart rate. Very important.
Make sure you have a day of rest in between your running days. My routine is 30 minute maintenance runs on Tuesday and Thursday, with Saturday my distance run. I also work out with a trainer at my gym on Monday, Tuesday, and Wednesday... that's my weight training. Sundays are my rest day. I'm running my first half in November, the Wine & Dine. Actually I'm running the Challenge - 10k on Saturday and half on Sunday. But this isn't my first race... just my first half.
Check out the runDisney website. Their trainer, Jeff Galloway, is a former distance runner and Olympian. And he's in his 60s and still runs. He's got really great tips for first time runners. And training schedules for races 10k and up. Look at them so you can see how many weeks he recommends for each race, the distances you need to run in training, etc. Plus, his schedules can be imported into your calendar.
Are you an annual passholder or DVC member? Next Tuesday is early registration for the Princess Half Marathon weekend in February 2017; regular registration starts Tuesday, July 12th. Check out the event and see if you'd be interested in registering for the 5k. You've got plenty of time to train for it. runDisney says that you must maintain a pace of 16 minutes/mile, but they don't check pace for any of the 5ks and I didn't see the pace cart for the 10k I ran in April. The Princess weekend is loads of fun. That was my first 5k in years and my first runDisney race. While their races aren't cheap, they are well organized, which I think is important for beginning runners. I ran my first local 10k in May and was disappointed at the lack of details provide to runners - no route maps (and a map, especially with hydration stations marked, is important), no race staff stationed along the route to answer questions/assist runners (important questions, like 'where's the nearest bathroom?'), etc. The last mile of the race was so poorly marked, some runners saw their times affected.
I'm concerned about your strict low carb diet, though. You need carbs for energy to fuel your muscles, especially for endurance activity like running. Do you do your cardio/weights at a gym? Does the gym have personal trainers? If so, ask one of them about your low carb diet and see if they can suggest foods that will help you feed your training but also meet your diet needs. And don't forget protein. You need protein within 30 minutes after a workout to help your muscles recover. runDisney's website also includes advice from a nutritionist. And she will include recipes. And of course, speak with your doctor to maker sure there are no problems with you starting a training program for running.
Apologize for the length of this response. There are several serious runners on the runDisney forum and they are excellent sources for advice, encouragement, support. Welcome to running. One you've run your first runDisney event, you will be hooked. And in a few years, you will be showing us your medal from the Doopey Challenge!
Take care
Sadly, physicians aren't well trained in nutrition in medical school.
