It's funny this has gotten so much traction and yet the OP hasn't checked in since shortly after posting the question in Oct. 2013. But for the sake of those that stumble upon this searching the forum, or clicking on links in Active.com emails, if I were the OP, I'd look at the general consensus of all the replies and slow down. From the sounds of it, you didn't have much of a prior history running, so you're going to have to build up to it. Just the way it is. If you were previously a runner, you can't jump back into cardiovascular activity and expect to pick up where you left off. And if your PT actually helped you maintain your cardio base, getting back out and running is a whole different animal and will take some adapting.
It's one of the hardest things for new runners to do, pace themselves. Get a heart rate monitor if you really feel lost, or you feel a disconnect between speed and level of exertion. The biofeedback provided by getting a sense of your heart rate while you train will help. Calculate your zones and stay in the lower aerobic range for a while (like months). And honestly, maybe I'm being an alarmist, I don't know how intense your PT was, but if you are consistently feeling lightheaded, go get a checkup with your GP and make sure you're all good to start an exercise routine. As a matter of fact, if you're just embarking on incorporating exercise into your daily routine, it's not a bad idea to get that baseline health check from your doc before you begin. Imagine how awesome it will feel, when you go back in 6 to 12 months and he/she tells you how great all your test results look! (Speaking of which, it's been 3 months since you posted. How are things going??)
As for breathing and form:
- Some of the breathing techniques mentioned here sound interesting, but at the beginner level, it may be putting the cart before the horse. I like the idea kreeseis mentioned of just getting into a rhythm. I find a little mindful breathing is good practice any time, and can particularly help one dial-in and relax on a run.
- Form, and what constitutes correct form, is a huge area of debate. I personally have found great benefit from working on it, in particular foot strike, posture & cadence. There are many resources, both paid and free that one can tap. Running specific shoes stores will often do free form clinics like NB Good Form Running. I've also done 1-on-1 sessions in Pose Running, but my personal favorite is ChiRunning. I have a background in Tai Chi, so I find the ChiRunning principles align well with my sensibilities. But you don't have to spend a mess of money, you can get a lot of information online that'll get you started. Once you find the approach that you have an affinity for, you can pursue it further with coaching, if you so desire.
Finally, you say you are doing a Couch to 5K. One would assume that means you are following a training program. That structure is important and will help you build towards your goal in a controlled, safe way. If you don't have a plan yet, there are tons of apps that can guide you through training and set a schedule for you. When I started running again after many years off, I used some of the free training plans on RunKeeper for iPhone and really enjoyed it. I particularly liked the 10K+ plans by Jeff Gaudette, but started with Mike Deibler's R4FL program. I've also heard great things about Jeff Gallaway's Run/Walk approach, but his plans on RK involve a fee. Though you can learn about his approach and practice the principles on your own. I still maintain a training log on RunKeeper, (as well as other sites), and it's been great to track my progress.
Hope you check in again and let us know how things are working out.