It does get easier!!
I started running earlier this summer, mostly to CC. Trust me it does get easier and you can go farther. I discovered its mostly mental for me. My legs get tired and my lungs get tired, so my brain says stop. I noticed if I can think of something else I can distract myself and keep on going. I notice if I can push past the initial discomfort/work, it all of a sudden gets easier. My body relaxes, finds its pace and I can keep on going. You may be going too fast. Try slowing down and settling into a nice rythym. Don't force yourself to run fast because you think everyone else is. I am by no means fast, I do about an 8 min mile (slows down to about 10 when I get tired), but I am working comfortably hard. If I focus too hard on running/speed/breathing it makes it so much harder. Don't fight it, allow your body to find its natural comfort zone. I find that my 1st mile tends to be the toughest, then I settle down and can keep going. That all being said, I think it took me about 3 wks to adapt to running and get my body used to that kind of work. I still don't do more than 5-6 miles at a time, due to knee issues that I don't want to recur, so I will never be any kind of long distance runner, but that is good for me. Give it time. I was surprised at how hard it was at 1st too. I thought "If I can do Cathe, then I can run, no problems" Its not the same type of work. Give it time and it will happen, I promise!!!
Nan