Leg and arm pains are often due to fracture or injury. Tendon problems, like tennis elbow, may stem from muscular traction (muscle tightness/repetitive use/external trauma) pulling on a tendon insertion and producing inflammation and/or tears, or from more gradual tendinous degeneration that sometimes occurs with age. Sometimes, a seemingly small injury, such as a minor fall, may lead to a severe, unremitting pain: touching the skin hairs, wearing clothes or feeling the wind on the skin may cause extreme discomfort. The extremity may have sustained color/blood vessel changes. This condition is known as complex regional pain syndrome (CPRS, also known as reflex sympathetic dystrophy/RSD, or causalgia). 
Along with medication management for various joint problems, conventional joint injections (steroid, hyaluronic acid) may help some joint issues, and newer, PRP (Platelet-Rich Plasma) injections may greatly help others (especially tendon issues). For significant anatomical issues, surgery may be preferred or required.
Most people are aware that acupuncture addresses pain in joint problems, but it can also address swelling. Additionally, both acute and chronic joint problems may respond to Chinese herbal therapy. For example, in Traditional Chinese Medicine (TCM), chronic tennis elbow/tendinopathy may be due to “Blood Deficiency”. Chinese herbs and dietary recommendations may help improve and prevent recurrence of this difficult condition.
Acupuncture, including ear acupuncture, and Neurological/Scalp Acupuncture (especially for CRPS) can be particularly effective in acute and chronic joint and extremity issues, as can Chinese Herbal Medicine, Trigger Point Therapy, and pharmaceuticals.   
These brief overviews of conditions represent distillations of basic and current medical reviews from the following sources:
 Conventional Medical Sources
- “Essentials of Musculoskeletal Care”. Robert K. Snider and Walter B. Greene. American Academy of Orthopaedic Surgeons & American Academy of Pediatrics. 2nd Edition. (2001)
- “Travell & Simons’ Myofascial Pain and Dysfunction: The Trigger Point Manual”. David G. Simons, Janet G. Travell, Lois S. Simons, Barbara D. Cummings. Lippincott Williams & Wilkins; 2 edition (1998)
- “Acupuncture Energetics: A Clinical Approach for Physicians”. Joseph M. Helms. Medical Acupuncture Publishers; 1st Edition. (1995)
- “Foundations of Chinese Medicine: A Comprehensive Text for Acupuncturists and Herbalists”. Giovanni Maciocia. Churchill Livingstone; 2 Edition (July, 2005).
- “Diagnosis in Chinese Medicine: A Comprehensive Guide”. Giovanni Maciocia. Churchill Livingstone; 1st Edition (January, 2004).
“Chinese Scalp Acupuncture”. Jason Ji-shun Hao, Linda Ling-zhi Hao and Honora Lee Wolfe. Blue Poppy Press; 1st Edition. (November, 2011)