I too had similar issues, maybe not as severe but I was lacking in general cardio.
I went to my first martial arts class and they did a 20 minute Curcuit and stretch.
The circuit consisted of:
30 sec jog on spot
30 sec sprint lifint legs really high
2 minutes stretching everything in the legs
50 squats
30 sit ups
30 leg raises
2 ninutes strecthing the entire upper body
30 knuckled press ups
followed doing all of this another 2 times
I was so sweaty after this and breathing pretty deep, however I decided to start biking more and more intense as id become quite slack, and attempt the above circuit atleast twice a aweek on non gym days. Seems to be working quite well I can now do all of it with a sweat yes, but without having to stop for a breath, without having to stand there for a few minutes after regaining myself.