Both my legs have began to become extremely tight along my calves when walking for even short distances and the symptoms all point to compartmentialisation syndrome.

I live along the Sukhumvit at Ekkamai and I'm considering Sukhumvit hospital, but I just want the best value and care for my money.

Are there any hospitals or clinics that specialize in orthopedic issues?

All hospitals have ortho departments and for any problem, the issue is not the hospital but the choice of doctor.

From what you describe I doubt compartment syndrome. For one thing, this usually occurs only after significant exertion, as in athletes, not after simple walking. At a minimum, you'd need to have been running for 10 minutes or so. Not walking normally. For another, it is far less common than the more likely alternatives, which are (1) peripheral vascular disease and (2) dependent edema. Neither of those are orthopedic conditions.

I suggest you start by consulting a vascular specialist such as:

Dr.Kritaya Kritayakirana - at Bumrungrad and also at Bkk Christian (latter will be less expensive, and it is on the BTS Silom line- Saladaeng stop)

Dr. Piyanut Pootracool - Bumrungard

Dr. Thamrong Temudom - Bumrungrad and also Bangkok Hospital