Last November I went to my doctor for what could turn into bronchitis.
Got a shot in the right glut. Result: no bronchitis, but increasingly painful sciatica.

How do I continue to practice? My MA is aikido.

Are you absolutely certain it's sciatica? Have you ruled out an inflamation of the SI joint?

The pain can shift to any location in the right leg from the glut to the top of my foot. Feels like a vise grip.

Sorry to hear it. I bring up the SI because of my own experience. Was misdiagnosed for two years with a diagnosis of sciatica, pain shooting down the left leg, past the knee. At times the entire leg would go numb. It's very hard to differentiate, sometimes, between the two (according to the specialist that solved the problem).

Hope it gets better.

Thanks, Harlan. So do I.
Glad you got your problem solved.

If you think you have sciatica, it could be due to your piriformis muscle being too tight hence irritating your sciatic nerve. This piriformis stretch in video http://youtu.be/2qZ517Rw7ME is the best I've seen so far because you can control the degree of stretch very well. I do this with my students in my Posture & Alignment class.

Knee crossing seems to work well when the pain is in the hip and upper thigh.
But what about when the cramping shifts to the calf and top of the foot?
At times it feels like if those areas were cramped any harder, they would shatter.

If you're cramping at the calf and foot, it could that those muscles are fatigued from overuse. Usually when we feel pain in any part of our body, we tend to stand, sit or move in such a way to lessen the pain. In your case that could lead to the overuse and fatigue of the lower part of your leg due to the unnatural motion or posture.

The quickest way to relieve a muscle cramp is to stretch it. For the lower leg, you could sit on the floor with your legs straight out and toes up. Grab the ball of the foot with both hands and pull back until you feel the stretch in the calf lessen the pain. For the foot, put the hand over the top of the foot so that the toes are pointing back to you and pull back ... this will stretch the foot on the heel end and actually can stretch the calf too. Alternate this for the toe end of the foot by trying to point the toes forward as much as you can by trying to get the toe, ankle and leg in a straight line (while still sitting down as above).

One other thing is to make sure you're properly hydrated by drinking lots of water. Water is essential for healthy fascia. Additionally I put a couple of drops of trace minerals in my water too. As one gets older, I feel it is more important to stretch the whole body. I usually spend about 30 min. a day doing specific exercises to stretch my myofascial lines and other myofascial release techniques. Today on the wrong side of 50 years old, I've become less interested in the high performance of my martial arts but more so in the functional performance and healing aspects of my training. I hope this helps you.

Thank you. It is really worth a try.
None of this happened before I received a possibly too deep injection in my right gluteus. And it is only my right leg which is involved.

Sort of an update. FWIW.
If I get to class a bit early and practice Jo kata for five to ten minutes, the cramping I feel is significantly less. :-)