Yes and maybe. Stress can cause headaches and panic attacks may cause sensation of shortness of breath or chest tightness. Don't know what you mean by lungs feeling full. Any physical symptoms need to be evaluated by your pcp to rule out disease before you make assumption symptoms are due to stress.
Yes. Anxiety can cause a myriad of symptoms from the headache you describe, to stomach pain, chest pain, flushing, and so on. However, to be sure this is what is occurring you should visit with your primary care physician and have an exam to be sure.