I guess that the meals themselves are probably not the most healthy and perhaps the meal times don't really work with when you want to go for a run? If you have access to a fridge you could try some of the following ideas...
Breakfast - overnight oats (google it, I have just discovered thease and am now a fan!). I use hazlenut or almond milk, started getting the UHT stuff which only needs to be in a fridge once opened so that saves on fridge space.
If you have a kettle you could make some flavoured cous cous (like the Ainsley Herriott ones) then just add some salad and some meat (unless vegetarian in which case substitute for appropriate protein)
If you go home on days off you could make up some different rice/pasta salads and then store them in your fridge and then add salad vegetables and meat...
First of all stop, take a deep breath and look at what you have achieved. You have gone from half a mile to 3 miles, that is 6 times the distance you started off with! Now the best speed to run at is the speed where you can still hold a conversation, this should help you to control your speed and maybe go a bit further.
You may feel slow but remember there many people who cannot run half a mile let alone 3 at any speed! Give yourself some credit!
Circuit training will also count as strength training as well as the speed from the shuttle runs. We are always being told to imcoporate strength training into our schedules in order to improve and prevent injury. I also find that doing a mixture of different activities just helps to mix things up and keep my training fun so I do the three triathlon disciplines with yoga, fitball and Spinning too which is good both physically and mentally.
In conclusion I would do both if time and circumstances allow.
I think that now you have considered the possibility of Asthma you should get it checked out. If nothing else you won't feel at ease until you've had the all clear (hopefully, I'm going for positive thoughts here!). Personally I agree with everyone that you may be making the classic beginners mistake of running too fast as well. Run at a pace where you can chat is a good guide. I have no idea about my breathing pattern and just let it happen naturally when running, the only time I think about it is during yoga.