Surprisingly, how you breathe while running can impact how often or intensely you get injured. For all runners, regardless of those with or without asthma, it is suggested that you breathe on an odd number count so that you are exhaling and inhaling on opposite counts. The most common and easy form of odd number count breathing would be a five breath count, in which the runner inhales for three counts and exhales for two. But how could this help avoid injury? Well, when you exhale, you exert a slightly greater amount of force on the foot that you land on simultaneous to your exhaled breath. So if you breathe on an even count, (i.e. if you inhale for two counts and exhale for two counts for a total of a four count breath) you will be landing on the same foot with each exhale. Over time, this can lead to a greater amount of force on that same foot, which can lead to many different injuries, from pain in your foot and ankle, to knee and hip injuries.

Having asthma can further complicate things though, as you are certainly aware. First things first, make sure you are regularly taking your asthma medicine. There are medicines on the market today that runners can take just before they start their run that will help calm their asthma. Then when you start your run, start with a warm up. You want to slowly increase your heart rate in order to avoid asthmatic symptoms. Be cautious against pollen and other air born allergens that can exacerbate your asthma. If the air is filled with pollen or other allergens, opt to take your run indoors on the treadmill. And definitely always run with your rescue inhaler. Consider purchase a belt or strap so that you can easily strap it to your body and never be far away from it. Finally, the main key to avoid asthma attacks is with interval running: running in such a way that you give your heart and lungs ample time to recover from increased exertion. This will ensure you don't fatigue your lungs too early.

Sources
https://www.womenshealthmag.com/fitness/running-asthma/slide/7
https://www.runnersworld.com/running-tips/running-on-air-breathing-technique
https://www.theguardian.com/lifeandstyle/the-running-blog/2014/sep/11/running-asthma-breathing-easy-pollution-pollen