Generally when I treat ankle problems I would use a combination of local points, points relevant to their tcm diagnosis overall and points that open the lower back all the way down the bladder meridian to the feet - so huatuo at L2, L5, S2, then perhaps UB 40, UB 57 along with tuina at the calf to release the achille and open the ankle. Possibly moxibustion around the joint itself. You can find many of the relevant points for pain within our acupuncture for arthritis article - in particular see the bottom of the article for local treatment points.
For appendicitis (in the future please create two separate forum posts - it helps people to find relevant information) the general tcm diagnosis is accumulation of damp-heat and toxicity so relevant damp heat clearing points can be used along with lanweixue the empirical extra poitn for appendicitis.
I tend to use empirical and tcm pattern specific points along with the following in most cases:
huatuo of T3 - lung/lymph/immune system</li>
huatuo of T11 (Left Side) - small intestine/intestines/appendix</li>
huatuo of T12 - intestines/transverse colon</li>
ST 11 - regulate flow of qi in abdomen</li>
SP 6, ST 36, CV 4 and various ashi points as appropriate</li>