One eye bigger than the other; what can be the problem and who to visit? (Photos)

You definitely need to see an oculoplastic specialist for evaluation. There are many causes of eye proptosis (bulging eye).   See video below.

Sudden increase in the size of an eyeball (eg. over the last 6 months) should be evaluated as soon as possible by an ophtalmologist. Medical conditions of the eye like glaucoma ( elevated blood pressure of the eye) must be rule out. Glaucoma of the eyeball could present without pain. Glaucoma is dangerous since it could affect the vision of the eye. Patients with any asymmetry of the eyes must be evaluated first by an ophthalmologist to confirm the eyeball (and vision) itself is not affected, before studying any other causes of asymmetry (like ptosis, etc)

Thank you for sharing your question and photos. In one photo you appear to have ptosis (drooping), but in the other photo you appear to have retraction (pulled up eyelid). See an Oculoplastic Surgeon for comprehensive evaluation and discussion of treatment options.Good luck,