There are many studies of twins trying to understand the unique connection between them. Your story is very similar to what many twins have reported about shared experiences across great distances. There is even a name for this phenomenon called nonlocality.
Nonlocality describes the direct influence of one object on another distant object. It is suspected that nonlocality is part of what is going on between twins. There is a twin study that has tried to answer the question of whether back injury or trauma predicts disc problems later.
The researchers studied 37 pairs of twins (all men) who were part of an ongoing Twin Spine Study in Finland. They interviewed the men about past back problems and history of injuries on every job they had ever had. The same questions were asked regarding back injuries during any exercise, sporting, or leisure activity.
Normally, there are 157 pairs of (identical) twins in the Twin Spine Study. The only pairs included in this study were those who had one twin with a history of back injury (or injuries) and the other twin with no recall of any back problems.
They did not find any significant differences in disc height or signal between the twins who had a previous back injury and the twin who didn’t. This was true for all 37 pairs. Twin members who lifted more weight at work were more likely to injure their backs but this did not seem to translate into faster or greater disc degeneration later.