My wife has RSD and or CRPS and can only draw from what I've witnessed. If it where me I'd research this disease and keep your eye on other conditions as well. Most of the time an injury is what sets this disease in motion but not all the time. Usually it is most prevalent in a limb and then spread to other limbs, but again not all the time. It can spread to organs, orally etc.
My wife broke her wrist and overtime the disease has spread to her limbs mostly. Sometimes she will complain about neck and lower back RSD pain.

What sets your daughter apart in my mind is other than a complicated birth she appears to not have had an injury, not to say that a very young infant can not get CRPS from very very early in life or that even an injury is even required.
The other thought is it sounds as thou your daughter has had spells of pain and swelling and then both pain and swelling totally disappear, many times over? How long ago did this start? How long does the pain last and does it infact leave altogether, no residual pain at all left until the next episode?