Acute Angle-Closure Glaucoma is unlikely given the lack of visual impairment, but
Dry Eye Syndrome or Irritation: The patient's symptoms started while cutting onions, which can cause eye irritation. The sharp pain on blinking and closing eyes, along with the location of the pain on top of the left eyelid, could be consistent with dry eye syndrome or irritation from the onions.

Blepharitis: Inflammation of the eyelids can cause pain, especially when blinking or closing the eyes. It's a common condition that could fit the patient's symptoms.
Conjunctivitis: Although the patient mentions no foreign body or visual impairment, conjunctivitis (pink eye) could cause eye pain, especially if it's viral or allergic in nature, and the patient has been exposed to an irritant like onion fumes.
Corneal Abrasion: Despite no visible foreign body, a small abrasion could cause sharp pain, especially with blinking. The patient did wash their eyes after cutting onions, which might have removed any visible debris.

Acute Angle-Closure Glaucoma: Although less likely due to the absence of visual impairment and other typical symptoms, this condition is an emergency. The pain on blinking and the specific location of pain could, in rare cases, be associated with glaucoma, especially if there's an atypical presentation.
Endophthalmitis: A severe inflammation of the interior of the eye, usually caused by infection. It's rare but can be vision-threatening and requires immediate attention.
Orbital Cellulitis: An infection of the tissues surrounding the eye, which can cause pain, especially with eye movement. It's a serious condition that requires prompt treatment.

Scleritis: Inflammation of the sclera (the white part of the eye), which can cause severe eye pain, especially with movement. It's less common and might not be the first consideration but should be kept in mind if other diagnoses are ruled out.
Uveitis: Inflammation of the uvea, the middle layer of the eye, which can cause eye pain, sensitivity to light, and vision problems. It's not as common as other conditions but is important to consider in the differential diagnosis due to its potential impact on vision.