Thanks for posting on HCM,
From your description it seems that you are suffering from a nerve pain
. If change of position by doctors could not provoke the pain, then it simply means you are having bouts of neuralgic pain and one of the nerves of your groin (possibly the inguinal nerve are having a problem). The problem might just be due to too much straining and compression of that nerve which then becomes pain or an injury
to the nerve. You will need to consult a neurologist
who can look into the matter.
If there is no obvious groin swelling, it will still be important to exclude inguinal hernia
(incarcerated or strangulated can cause pain). Your hip joint could also be strained as to generate pain around your groin. Another rare possibility is psychogenic pain (pain which comes from your mind and is not related to any part of your body being in distress).
Hope this helps and wish you the best