Stress reduction techniques practiced when not under stress will help you be able to put those skills to use when you need them while under stress. Techniques often include relaxed breathing, visualization/guided imagery, or progressive relaxation where you sequentially tense muscles and then release them.
Practice diaphragmatic breathing - Then when feeling stressed do 1 or 2 relaxed breaths with the diaphragm.
Progressive Relaxation - Learn the feel of how to release tightened muscles, by contracting each muscle group beginning with the feet, hold the contraction a few seconds, and then relax the contraction feeling the circulation return to the area. Progress up the legs, trunk, shoulders, arms and face (including your forehead by raising your eyebrows). Then when feel stressed, contract your shoulders/upper traps/face and release them as you exhale.
Reducing stress is a big factor in keeping fit so it is good that you have recognized it as something you need to deal with. The Relaxation and Stress Relief Workbook is very good in helping you identify your stress and then learning to manage it.
One other thought. My Tai Chi instructor describes the need to make sure that your blood is circulating and draining out of the head. He describes that feeling of “fullness” that you mention as the congestion of blood that comes about when you focus on mental concentration, (much as you increase circulation to a muscle when you exercise). I don’t know if that is an accurate scientific explanation, but it is amazing how you can get the sensation of tension draining out of your head when you focus on allowing your chi and blood to circulate. I learned that from one of Bruce Frantzis' instructors in the Taoist Longevity Breathing Class.
And you are right that exercise is a great stress buster. Hope those ideas help.