Beta minor can usually be detected by the CBC and electrophoresis. Alpha isn't always identified easily and if suspected, a DNA test may be needed to diagnose it.
Poor circulation can cause the mentioned symptoms of chills and aches, and this is a characteristic of thal minor. However, it is also symptomatic of other anemias, vitamin D deficiency and thyroid disease. I encourage all to get their vitamin D level checked, as it is low in over half the world population. If low, get the level up to at least 35. Natural vitamin E can help improve circulation and vitamin C can promote blood vessel health.