Hi Ceri,
Great that you have set a realistic goal of a half marathon at the end of next year. This is realistic and spot on. I suggest along the way you get a few 5k or Parkruns in and definitely a couple of 10ks over the summer.
The breathing has been mentioned in Jan's answer above. Remember the harder you work in terms of effort level, the more strained the breathing becomes.... this is normal! At this point you have to ensure you just get the air in! Breath hard, breath loudly, snort.... whatever it takes.... just get the air in!
Top tip for winter running is, get kit that deals with the cold weather. Technical running base later, windproof light weight running gillet, running gloves etc. Saucony Vizipro gillet in bright pink is awesome and has flashing lights on it! No chance of being missed in the dark! Zests Nicols Davenport has her eye on one!
Build up the distance gradually and my top tip is run to TIME NOT MILES. ie 45mins, 60 mins etc. Your long run each week should never increase by more than 10-15minutes and every 3 to 4 weeks should be an easier week where the long run grop backs.
Concentrate on different paces throughout the week, particularly threshold in order to build your fitness for those last few miles in your half marathon. All my schedules have this type of work in and build people up safely and gradually. Again check out RunLounge.com.
Good luck!