First, congrats on the weight loss and getting into running. I did the same thing 4 years ago, and yes, it is very addictive.
The advice that zrx and flyinguy gave are spot on. When I started running, that's all I did-run. I got quicker by just putting miles in, but I got BETTER at running by doing strength/core workouts and cross-training. Working your non-running muscles is important to both get quick and (more importantly) reduce the risk of injury.
If all you have is 3-4 days/week to train and you're using them for running, adding 10-15 minutes of pushups and situps on each of those days will help you more than you expect. Lunges and squats are easy to do any time as well. Biking and swimming, as mentioned, are great cross-training workouts. If time is an issue, do a spin class and add paddles to your swimming for a more intense workout.
As you're planning on a trail half in October, make sure you add trail runs to your routine if you haven't already. Any idea what the course of the trail race is like? Some "trail races" are on gravel bike trails and are basically the same as running on pavement. However, some are on actual hiking trails, like the Laurel Highlands Hiking Trail (not far from Pgh), or Appalachian trail. If possible, make sure you train in an environment close to what you'll be racing in.
BTW - if you don't want to "cross train" per se, trail running on actual trails where you have elevation changes, rocks, roots, etc. is a great alternative, as you get a better all-around workout of your legs, core, arms, etc.
Let us know how you do in your 10k - you're ready for it now and will do just fine. And feel free to post in this thread or send a PM if you have any questions.