I agree with kenkeith. You need to go to the doctors to rule out anything serious. Don't delay doing this. Go.
However that doesn't mean i think there's anything wrong with you. Your symptoms could just as easily be panic related. Go to the doctor to be sure though.
If it's panic there's lots you can do. One thing is learn to stop over breathing (which can make you feel like you cannot breathe when in fact you have too much oxygen)
You have symptoms that may be panic related. Shortness of breath and a dry cough caused me to go to ER, and I was shocked to hear I had a heart problem. You should consult with your doctor to rule out anything serious