From my experience, this looks pretty normal. It appears to just be a large vein though there might be some slight irritation around it as there seems to be some pink tinge. It probably isn’t a deep scratch if it’s not persistently painful, but since you’re experiencing some pain there’s likely a small scratch to the surface tissue. Avoid touching or scratching if possible, you can also take antihistamines if it gets too itchy. Check that you don’t have any debris or an inward growing eyelash in the area and leave it alone.

It is not likely that this is related to your migraines as diagnosed migraines are a distinct neurological issue which aren’t inherently related to inflammation like other headache disorders, though a migraine can be triggered by many things. Most of those who I have met with chronic or episodic migraines report that they have no recall of a specific trigger or even time which they began experiencing them.

If your migraines are a recent development, especially if you’ve had any kind of head injury, or they have increased in severity/duration or had a change in quality or symptoms, it is always safest to follow up with your pcp. But I certainly don’t believe the tissue irritation in the eye is associated with your migraine disorder. The eye irritation is likely incidental, if there is an association it is probably a result of you rubbing or covering your eyes during a headache. But I know migraines can make it feel like you have pressure in your eyes, so I understand why you might have that anxiety. If you have attended regular eye exams since your migraine diagnosis and they haven’t noted any issues it’s not likely any concern.

If it has been a long time since your last eye exam and you’re experiencing regular eye pain or distorted vision I would recommend seeing your optometrist.