Hi Ian K and welcome.
I am so sorry to hear of the miserable way that you have been feeling in the mornings.
Morning anxiety is not uncommon, so know that you are not alone with this issue.
It is tricky when we have a physical issue such as GERD that is exacerbated by anxiety...and then the cycle of symptoms/more anxiety/more symptoms starts up.
I think that a two pronged approach, as you are seeking is a good plan.
Keep working to treat your GERD. (have you checked in with our GERD forum here for advice?)
...and yes, there are a lot of things that you can do to lower your anxiety. I am going to post links below from our Resources for you to chedk out.
Self Help sites with breathing/relaxation exercises instructions
Panic attack relief exercises:
http://www.healthcentral.com/anxiety/c/73076/34334/breathing-lessons/
http://www.healthyplace.com/
http://www.stress-relief-exercises.com/
http://www.ehow.com/video_4405003_breathing-exercises-panic-attacks.html
http://www.psybersquare.com/anxiety/panic_relax_I
Books for overcoming Health Anxiety:
http://www.amazon.com/Feeling-Good-New-Mood-Therapy/dp/0380810336/ref=sr_1_1?s=books&ie=UTF8&qid=1379950432&sr=1-1&keywords=Feeling+Good%3A+The+New+Mood+Therapy+by+David+D.%2C+M.D.+Burns
http://www.amazon.com/Overcoming-Health-Anxiety-David-Veale/dp/1845298241
http://www.amazon.com/Treating-Health-Anxiety-Cognitive-Behavioral-Approach/dp/1572309989
Give the stress relieving exercises a try...and check out the book recomendations.
This is a good start. However, if you feel like your issues are more than can be handled at home...don't hesitate to talk to your doctor about the possibility of seeking therapy. I benefitted so much from this treatment option, and we have some similarities in our stories!
Keep talking with us as well. We are here to listen and care anytime...support is key!
Scaredy Cat