Yes 'Complicated Migraines' is just what the term indicates, complicated or complex meaning there are a lot of different forms of migraines all in one condition it seems! The facial droop is an Autonomic symptom and so is the eye droop which is usually found with Cluster Headache but can be found in migraine too! I have the eye droop myself and it can look as if I am starting to have a stroke if I am having a bad attack!!!
The loss of power in one side of the body usually comes along with Hemiplegic Migraine and can often be mistaken for a full blown stroke! It sounds as though your Neuro knows his stuff and you should get good support there. You are not the only one that suffers like this, but there are not as many of you as with the more common forms of migraine!
Please feel free to keep asking questions, take care
Co-Moderator of the Migraine/Headache Forum