Lately I've been trying to do cardio for at least half an hour about 4 times a week but I keep having to stop every 5 minutes to catch my breath because I get that painful constricting feeling in my chest that makes me want to throw up
Before now I've NEVER done cardio before (In the US I pretty much sat around on my butt) so I'm not used to it. I know that if your body gets used to it it'll get less and less painful each time but I've been at it for about 3 weeks and it's still the same.
Is it less effective if I keep stopping to rest? Is there a stretch or a cool down exercise that can make that constricting feeling go away faster? And also for reference...what are other methods of cardio? Because all I've been doing is jogging on a treadmill at level 8.7 (I dno if the levels are universal) and using the bike machine at level 13 and usually before I start I use some weight machines first like the ad/abductors, eagle arm press...or should I do those after?
I know jump roping is one
I'm trying to do my best to lose fat + gain muscle at the same time -.-; It's been really hard so far and I know it's normal but it's SO disheartening to see that I only lost 1 kg a week after all that pain and sweat

take it slow. start with moderate intensity running. you will know how much 'moderate intensity' is as you try out different speeds and see how long you can run at that speed. try running at 6, and see how long you can go. if you can go 30 minutes on it, then try 6.5.
keep in mind that there are different types of endurance, and this one will be working your aerobic endurance. this will allow you to run for longer stretches while you BREATHE, and let your body burn carbs/fat using the oxygen you take in your body.
in order to raise this type of endurance, try running SLIGHTLY faster, and then slightly slower when you need to rest a little, and keep alternating between these two. don't push yourself too hard, or you'll end up getting into anaerobics, which i will mention next. but to wrap up aerobics, just keep alternating between moderately-high intensity to moderately-low whenever you need, and be sure that you dont run out of breathe and you keep running.
next, this is your anaerobic endurance. this is sort of what you are doing, but a watered down version. you're running at higher intensity, and causing yourself to lose breathe in 5 minutes. this is too long. get off the treadmill, and find a track to run in. what you will do is jog a few minutes, and once you're warmed up, you will alternate between VERY HIGH INTENSITY SPRINTS and walking.
basically, you will sprint for 20 seconds, and walk for about a minute, and keep alternating. keep in mind that this 20 second sprint is the absolute fastest you can go. and dont worry if you can go full 20 seconds. keep pushing but stop if your body tells you to. but by doing this, you will allow your body to do high intensity sprints for longer periods (which honestly will amount to seconds, but it makes a bit difference in the long run).
furthermore, these 'wind sprints' will increase your capacity to take in more oxygen and replenish energy, and thus cause you to be able to do aerobic exercises at higher intensities for longer periods of time.
the best way to go would be to alternate between these types of exercises. work on aerobic endurance twice a week. and anaerobic exercise (wind sprints) another couple of times a week. this is to keep your body from getting too adjusted to one kind of exercise.
on a final note, be sure to include strength/resistance training into your exercise plan. this is what will build up your muscle and also replace muscle lost when you are doing cardio.
good luck!