In my experience this sounds more like an anxiety disorder than panic attacks. Panic attacks are usually very acute and can be serious enough to call an ambulance. Anxiety attacks tend to be lower grade, but last for days or weeks at a time.
I don't know how you've gotten this far without medication. I was in the emergency room the first day. If you have not gone already, you need to see your doctor. You need to get an EKG and blood test to rule out certain medical conditions. You may or may not need medication, but if you do you need to be careful because some of them are extremely addictive and should not be taken for extended periods of time.
The next step is modifying your lifestyle. If you can, clear your schedule for a few days so that you can sleep and relax. Exercise (walking or other low-impact) during this time, since movement seems to help. Examine your life to determine what may be causing the attacks. Anxiety attacks are often brought on by things like overwork, concern for your family, poor personal health, and drastic life changes.
If you drink a lot of caffeinated beverages, eat a lot of fast or processed foods, or just generally have a poor diet, chances are that adjusting it will help. I went from drinking somewhere around a half dozen cups of caffeinated tea per day to the same amound of herbal tea, and from fast food burgers to healthier home-cooked meals.
Hope this helps
Dal