I did the ex-swimmer thing to, and my first forays into running weren't all that successful either. I guess I just expected I'd get the hang of it like I had swimming, forgetting all the junk yardage I'd put in to hone my swimming.
Wanting to stay away from the gym poses some additional challenges, since it is difficult to maintain one's resting metabolism without some strength training, and this can contribute to slowly finding your program less effective. Your feeling you've hit a plateau may be due to this, especially if you are running at about the same speeds every run.
If you are going to stick to cardio alone, you will need to figure out how to make the most of it, training different aspects of your cardio performance as you did when you were swimming. That means some sprinting/intervals, some high-intensity but still aerobic, and some longer, slower sessions. This will improve your cardio fitness faster, allowing you to do more work in the same time and burning more calories.
The interval work will have some muscle growth benefits, although nowhere near what lifting has. It also boosts your metabolism for hours after you stop exercising as your body attempts to repair from the stress you placed on it. Still, I think you'll find a fairly broad consensus that strength training is critical to really seeing progress in your physique.
You'll also hear lots on low-fat, high-carb diets. Having had my gallbladder out last year (all the men in my family end up w/ severe gallstones for some reason), I know that eating fat can cause interesting side effects for at least a while. You should make sure that you are getting good quality fats at least, taking fish oil supplements and olive oil.
Likewise, make sure you are careful with the carbs, trying to limit the ones with the big impacts on your blood insulin levels: esp. sugar & sugar substitutes, white flour, and the like. Rice has a high glycemic index (search the site or google it if you don't know what this is), but doesn't have much of an insulin impact. Whole grain oats, buckwheat, real whole wheat (many "wheat breads" and multi-grain breads are largely white flour).
All this is hard to do if you don't cook, as processed ready-to-eat microwave food is often loaded with junk. Eat lots of small meals rather than a few big ones. Eat foods with lots of fiber, and get some protein and fat at every meal. The fiber, along with high water content in foods, give the feeling of fullness with fewer calories. The protein & fat help slow down when the meal leaves the stomach, and all can help keeping your from hunger induced by blood sugar spikes and crashes.
Keep a log of your food intake and calories, as well as your calories expended to make sure you aren't underestimating your intake relative to your expenditure.
And definitely reconsider some type of strength training. If you search this site, you will find some non-traditional strength programs that can be done without a gym.