That works too, of course. But 'la' is often used as a replacement for 'mia'. For example: "Mi vizitos la gepatrojn". If the context doesn't indicate otherwise, this would mean "I'm going to visit my parents"
Wouldn't it be better "La tuta korpo dolorigxas"? I don't know if I understood the whole "ig" and "igx" thing correctly.
Has a different meaning. What you propose sound to me like it your body is the one feeling the pain, which not being incorrect it does sound extrange. La ReVo says that it means "senti doloron" and vortaro.net does not list it. I would believe is not the standard form of expressing oneself.