Only having a prominent set of eyes is not diagnostic of hyperthyroidism. It causes changes in eyes at later stage of disease.
For you to develope ophthalmopathy you must have other symptoms of hyperthyroidism as well.
To cut the story short, see an ophthalmologist ASAP, and get your check up done. You can do your
thyroid hormone levels in the meantime.
Next Steps
T3 ,T4,
TSH levels
Eye check up by ophthalmologist