Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Seek emergency care if new eye movement problems occur with severe headache, weakness, numbness, confusion, difficulty speaking, loss of balance, major head or eye injury, or sudden vision loss.
Children should be assessed promptly because untreated amblyopia can affect long-term vision.
Seek urgent medical care for a sudden new restriction of eye movement, especially with double vision, eye pain, a drooping eyelid, or a pupil change.
A congenital condition does not usually begin suddenly, so another cause must be excluded.
Arrange a routine eye assessment for limited eye movement, a repeated head turn, eye retraction, eyelid narrowing with movement, or eyes that do not point in the same direction.
Make a follow-up appointment if a known condition causes increasing neck discomfort, trouble at school or work, troublesome double vision, or changing alignment.
Every sign above is quoted from the sofidex article on Eye retraction syndrome. If you are not sure, err upward — it is always reasonable to be checked.