Answer: Orbital pseudotumor.
Step 1: Proptosis with restricted ocular movements points first to thyroid eye disease, which is the most common cause of unilateral and bilateral proptosis in adults.
Step 2: The key word here is euthyroid. The patient has normal thyroid function, so thyroid ophthalmopathy becomes far less likely as the explanation.
Step 3: In a euthyroid patient with painful proptosis and limited movements, the best fit is orbital pseudotumor (idiopathic orbital inflammatory syndrome), an inflammatory mass with no infective or thyroid cause.
Why not the others: Orbital cellulitis is infective with fever, lid swelling and toxaemia. Orbital lymphoma is usually a slow, painless salmon-pink mass. Thyroid ophthalmopathy is excluded by the euthyroid state.
Ref: Comprehensive Ophthalmology, A. K. Khurana, 6e, p. 335.