The shortness of breath you mention is pretty common, and probably due to you chest breathing.
You can work out if you are chest breather by doing this exercise:
Either sit up straight, or preferrably, lie down. Place one hand on your chest, and one hand on your stomach.
Don't focus on your breathing and just let your breathing stay natural as it was. Watch your hands rise and fall. What one is it that is rising the most? If it is the top one, you are chest breathing.
Some people can change breathing when anxious - so it can help to be conscious of your breathing when you feel anxious.
You can practice stomach breathing so that when you feel yourself get anxious, you can make yourself breathe steady and from the stomach - this can help allieviate anxiety before it's gripped hold.
Again, welcome to the group.