I used to work for a pharma supporting a system that does exactly this. All pharmas have a system like this mandated by law. It's called adverse event tracking. You tell your doctor "I had effect D while taking drugs X, Y, and Z". The doctor reports this to the pharmas that make X, Y, and Z and it is all tracked for potential causality.
The difficulties arise if there are too few people who have that side effect while taking that combination of medicine. If the occurrence is too rare there isn't enough statistical data to show causality. That's why all the commercials say "side effects may include ..." because some portion of patients on the medicine had those symptoms and causality may not be determined.