Many. Muscles of the arm include the biceps, triceps, brachioradialis, the extensor and flexors of all five digits, including my favorite, the extensor digiti minimi (the muscles that extends the pinkie finger.).
What is causing my muscles in my right arm to be sore when I stretch out my arm and also cause a pins and needles sensation in my hand?
Vague. Could be a pinched nerve, stress, hard to say. I would see a doctor asap to perform a thorough history and examination, tests, etc.