There are many causes for sneezing in birds. Parrots do sneeze and it is a normal . Most parrots come from tropical, humid climates and when kept  indoors or places were humidity is very low.  The nasal passages gets dried, which, in most  cases is the cause for  sneezing.    
 A Parrot may sneeze for a number of reasons other than due to environment being  too dry. Vitamin-A deficiency or a bacterial, fungal  or viral infection can also cause sneezing and discharge from your  bird’s nares.  
But frequent sneezing with a wet nasal discharge is an indication of illness. The nasal discharge causes the nares to get wet or blocked, which in turn causes irritation resulting in sneezing. It could be due to bacteria, fungi and Chlamydia. Clinical test are to be done to confirm the cause. 
A more serious problem that could cause damage to the  nasal or sinus passages could be the case if audible breathing sounds,  tail-bobbing, weight loss, nasal or eye discharge or a change in  vocalizations or eating habits accompany the sneezing.
At times it may not be due to sickness but due to the environment. . Correcting the environment will solve the problem. The most common cause is deficiency of Vitamin A, in birds that are on all seed diet. Low humidity and lack of proper ventilation is another cause. 
Sneezing due to sickness maybe due to wide range of causes, The causes could range from Fungal or Bacterial infections Aspergillus or candida. It could also be due to Mycoplasma infections or Chlamydiosis (Psittacosis) Malnutrition, especially vitamin A deficiency. Cyst / Tumors inside the intranasal passage can block the Sinus passage causing irritation leading to sneezing. It can also be due to mucus or seed husk lodged in the intra nasal passage, . Dusty seeds can also be a reason. Birds are allergic to Dust, Cigarette smokes, Sprays and Teflon fumes and feather dust 
Birds that have feather dust (Cockatoos) should never be housed with birds that have oil glands (Macaws). For example Macaws are allergic to Cockatoo’s feather dust. Sneezing is an initial sign of an underlying sickness. So regular sneezing should not be taken lightly but should be attended to promptly.. All cases of regular sneezing in a bird must be attended to promptly.
Viral infections in birds rarely cause sneezing. Usually viral infections in birds cause serious disorders like conjunctivitis which is accompanied with sneezing. 
Depending on the findings the parrot should be treated accordingly. It could be as simple as increasing the humidity to bacterial or anti fungal treatment or both. Nasal irritation causes the bird to scratch its nostrils most of the times it is not due to very serious reasons. It can be due to dust allergy or a seed hull lodged in the nostril and it  is usually blown out while sneezing.