It is a good idea to have the vet check this out.
Are the eye rims fully pigmented?
If not that may be the source of the "always" been like that.
I would guess that it is not allergies since the puppy is 5 months old.
Possible but rare...cause it takes time for antibodies to develop and the average age of when a Maltese presents with food allergies (which this symptom might indicate) is around 3. Possible environmental alegies are the cause but..
bottom line
check with the vet.