It is very likely for ophthalmoplegic migraine patient to have droopy eyelids.
When the patient suffers from ophathalmoplegic migraine, also called ocular migraine, in which the pain focus on eye regions, temporary eye muscle weakness or paralysis occurs. As a result, the muscles can't raise the eyelids well. This is how ocular migraine causes droopy eyelids.
Well, in my opinion, migraine cannot lead to droopy eyes. Generally speaking, according to some experts, when you have migraine, some other symptoms such as eye twitching, a harsh bilateral headache experienced at the backside of the head may occur too. And also, visual aura, temporary partial vision loss, and nausea can be possible. But on the other hand, for droopy eyes, it can be caused by weak levator muscle, paralysis of some nerves, even Injuries such as fracture of the skull bone between eye socket and nose. So I have to say that migraine cannot lead to droopy eyes.
Alright, I am so sorry to hear that news. According to what I know, it is possible migraine or severe headaches might lead to droopy eyelids. But that is just temporary, caused by the symptoms of migraine. What you gotta do is to take medical treatment right away and take adequate sleep. In addition, small amount of exercise would be good.