Congratulations on the 10 minute milestone! That is fantastic!
I have been running for about 6 years now, and I finally do not giggle when I call myself a runner.
I love it. When I started I could not run for more than 3 minutes and even then I was staring at my watch convinced that I had encountered a small tear in the time-space continuum. It was awful. It stayed pretty hard for a while, but I lived off the accomplishment I felt at the end of the run. Eventually, I found that if I was consistent it actually got easier and I started to enjoy it even
during the run. I thought that only happened for those skinny bitches in their boy shorts and jog bras. Nope, it is for us mortal folk too!
I found that I like doing running events and I have run a lot of them. I am a tad bit obsessive at times. I prefer running on trails, while harder due to hills, are much more enjoyable due to scenery. "Pretty" will distract me from just about anything. I am currently training for my 13th marathon in Portland in October, which is a road marathon, but in a city I have never been to so I am excited.
I love talking to runners, new and experienced and have had the honor of running many first 5ks, 10ks, half marathons and marathons with new runners.
I am
UBER excited about this thread. (I will calm down, sorry

)
Oh and as for breathing rhythm, slow down. It may feel like you are running WAY too slow and just shuffling, but you can get into a rhythm with your breathing and go longer distances. Eventually, by virtue of increased fitness, you will get faster. There are other tricks to getting faster, but I would focus on getting distance and fitness first and then work on speedwork. Just my 2 cents. I am by NO means an expert, but I have a hell of a lot of fun when I run.