I'm a big fan of Vibram Five Fingers shoes. People in America (including myself, even though I love to wear them because they feel so good) tend to think they look very odd but people in India were very fascinated with them and told me they looked cool. This linguistic quirk seems to fit in with all that somehow.
It is not standard English to say "I am having pain". Most people would say "I have a pain ..." I think, if you had a recurring problem, (meaning that you have it, and then you don't, and then you have it again, etc ) then you could say, for example, "I'm having headaches all the time ... ". In this case, it means that your problem is "having pain", but perhaps at that very moment of saying that you are having pain, it could mean that you don't feel the pain. It is like saying "I"m taking a Hindi class at school." At that moment you might be at home talking to someone on the phone. It means that during the current year or semester you are enrolled in the class. Another example would be "I'm having a party" (maybe next week). Or "I'm seeing a doctor about my problem of having pain." In India it is quite common to hear people say things like "I am having a book and a pen", but this is not correct English. When we refer to possession, we say " I have. (I have two brothers. I have a small house. I have a motorcycle.) An example of when to say "having" is when you are hosting an event or arranging a situation. "I'm having friends over this weekend. I'm having an exchange student come to live with us for half a year." 'I'm having my house painted.' Hope this helps explain some of the problems of "having".
I agree with your remark. It is even worts in french cause we do not have the progressive present. But... If we want to express a chronic pain, I think that "having pain" would be more specific to describe a recurant pain, not a one time discomfort like when you shoot a chair leg bearfoot.