Completed the first run of Week 3 tonight....my legs can cope but it is breathing that is proving my problem. How can something I do every minute of every day be so hard?? If my breathing is too shallow, I struggle, if I breathe too deeply, I feel like I am going to keel over. Only at the last part of the second 3 minute run did I finally hit the perfect rhythm and did it make a difference.
Breathe, breathe, breathe.......
I think you could be pushing too hard for this stage. I suggest you try to relax and slow your pace a little. You say the last interval is better and I think by then you have settled into a rhythm. I also find the first 10 minutes of a run my body is still warming up and getting used to the idea of running. Try easing off I hope this helps.
I too struggled with my breathing at the beginning but I am now on week 9 and my problem is aching calves, breathing is absolutely no problem! Trust the programme because it really does work, I had done no exercise for years but can now run for 30mins.
I struggled with my breathing too but happierswimming gives some great advice/tips for mastering the technique. Click on the breathing tag and have a look for her blog as I suspect it could be helpful reading.
Good luck for your next run, you are doing great! 
the breathing didnt fall into place until week 4 or 5 for me, which is also where everything seemed to click together. please dont worry too much & as mrslazy says, you may be running a little too fast.
good luck x
Week 3 run 1 and scared. 
Week 3 Run 1 Failed ‼️
Week 3 Run 1 completed
Week 3 Run 1 (again 🙄)
Completed week 3 run 1
