Sing to yourself. It forces you to breathe and stops you holding your breath. Swimming is great for fitness with low impact and helps train your lungs and body to improve your breathing. Spinning and the elliptical are also super low impact options!
Swimming is a great one for me. I have knee problems so much running isn't really an option for me at the moment. I focus on getting into a rhythm and keeping my time between breaths regular before slowly adding another stroke in between taking breaths to push myself a little more. I do the same when I'm warming up with horses. For the first 10 minutes I work on mine and the horses rhythm. Eventually it just becomes second nature.
Different breathing exercises can help to increase your lung capacity. For example, belly breathing : lie on your back and place both hands on your belly. Inhale and focus on allowing your abdomen to expand out and up as much as possible... your upper chest won’t move until the very last moment of your inhale. As you exhale, feel your belly button reach towards your spine and your lower ribs knit together. Repeat for 5-10 breaths
Just remember to keep breathing deep breaths!
Ab, back and core strengthening exercises. Also do swimming as this will increase cardiovascular endurance and build muscle from the water resistance.
Also, breath deeply and relax.
Try doing interval training or look online for cardio workouts that don’t involve running.