Yes, migraines will cause swollen eyes. Technically, a symptoms seen in some migraine sufferers is puffy eyelid, also called eyelid edema or oedema. It is considered a unilateral cranial autonomic symptom. Puffy eyelid doesn't occur in everyone with migraine, and it's more common in cluster headaches. And sometimes it is related with other disorders, such as allergies and tiredness.
You can check if your swollen eyes is caused by migraines or those follow reasons:
Allergy. Some immune systems over-react to a foreign ailment such as pollen or dust triggering symptoms of puffy eyes.
Sinus infection. An abnormal mucus production leaking from the nasal passages, provoking inflammation in the sinuses can cause puffy eyes.
Cosmetic surgery. The aftermath of cosmetic eye surgery or botox applications to the face may cause puffiness.
Changing conditions. Puffy eyes are usually a temporary condition that can be from lack of sleep, changing in hormones or weather alterations.