Hello Caroline,
She doesn't sound too well.
Can you pick her up and listen carefully to her breathing? Does her breathing rattle? (called tracheal rattle), does it sound almost bubbly?
Chickens are very prone to repiratory problems and whilst they can simply catch a cold, more often than not it is a bit more serious than that.
Sneezing birds usually have an upper repiratory problem and there can be discharge from the nose with this as you describe.
There can be a number of causes - poor ventillation (droppings give off ammonia), sawdust (larger wood shavings sold in pet shops usually has the 'dust' extracted to prevent these problems), viruses - such as infectious bronchitis, pneumovirus, fungus (aspergilliosis), mycoplasmosis, infectious laryngotracheitis, Avian Influenza (one of the many variants), Fowl pest / Newcastle disease, Coryza to name some. All of these conditions show very similar symtoms.
The fact she is nodding off suggests to me it isn't a sawdust problem.
It is possible with veterinary testing (which can involve live birds as well as dead) they can come up with the answer but this would be an expesive and most vets (in my opinion) would just prescribe a broad spectrum antibiotic (such as Baytril or Tylosin) to treat the secondary bacteria infection that usually follows and is the cause of the symptoms we see.
Isolation is the first thing I would consider and good ventillation- If you have ACV (
apple cider vinegar for chickens article here) add this to her water (2% dillution) this will help cut through the mucus, to help her breathe and is a good all round tonic. Personally I use crushed garlic in the water too - but this really needs a long time to build the immune system and doesn't work quickly.
I'll keep my fingers crossed for her and hope it isn't too serious.
Tim.