I am sorry you are having so much trouble. coming to terms with having Sjogren's is lifelong process of adaption to the illness.
If meditation works for you, and enable you to continue on, that is great. It apparently is working for an number of people who posted here.
However, my first impression was more in agreement with what grammad97 said: "I purged all I could from my life in the way of tasks and chores." So I would suggest simplifying your life as much as possible just as grammad97 is suggesting.
For migraines, if you can catch the migraine at the very first hint of getting one, I have had success in killing them with two excedrin migraine tablets, or two anacin migraine tablets. Both are loaded with caffeine however, so if you take them plan to be awake for some long time afterward.
Perhaps your doctor might have a more effective medicine for migraine. There is a medicine called Decadron that you could ask your Rheumatologist about, but do not take this longer than about three or four days maximum - if you take it long term you can get deathly ill as it is a super strong steroid.
As for the slow digestive system - yes, that is a typical Sjogren's problem, as is the fatigue the makes exercising difficult, which would presumably help things move through your system. There are several tricks that work quite well for this.
The first one is to bring your knees up to your chest several times when you wake up in bed in the morning. This definitely squeezes one's abdomen and promotes movement of the system - a natural approach. Also any exercise during the day helps - any exercise, small things, just bending over, doing one deep knee bend. Find little ways to stretch and move - you don't need the full gym workout.
Beyond physical movement to promote intestinal movement, Metamucil - the orange powder, can potentially work brilliantly if taken in small amounts, such as a rounded dinner spoon, a teaspoon that you use in your coffee cup and not a measuring teaspoon. It works sufficiently well that you don't want to take too much.
If you really get jammed, Phillips Milk of Magnesia will break through anything, although it is kind of extreme and only to be used for the more extreme situations.
These three approaches, seemingly simple but learned after years of trial and error, will set things right even if you only eat doughnuts, ice cream, and potato chips as your three main food groups.
So the fourth secret to ending gastroparesis is to eat a healthy diet and get regular exercise. There are secrets to help practically implement this as well. One huge unknown fact is amazing: the more you eat vegetables, the better you like them. The implication of this is to make the effort to force yourself to eat vegetables and fruits that you normally don't eat. Not only do you end up liking them, but they become your favorite foods. You then lose weight, and also eating salads, fruit, and vegetables in place of faster foods help tremendously with gastroparesis. I suspect that even with Sjogren's, if you ate a really healthy diet, the gastroparesis would largely vanish, enabling you to reduce the amount of time that you take Metamucil.
Both school and work are inherently stressful. Being sick with Sjogren's Disease is also inherently stressful. You probably have various options, like puzzle pieces you can move around. I have worked full time and pursued graduate degrees full time simultaneously, with the advent of Sjogren's, by the way, so I have some insight into the stress that you are talking about. One might shout it loudly: STRESS!!!!
Dropping work, dropping the Master's, and/or getting better treatment for any symptoms you have of Sjogren's Disease would help you.
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Good luck and keep us informed as to how you are doing!