As always the information offered here is to provide guidance and is not intended to be a substitute for the good advice provided by your own avian vet. When in doubt always consult your own veterinarian.
Just like humans, cockatiels can also suffer from allergies. Some signs of allergies in cockatiels are wheezy breathing, sneezing a lot, and watery eyes. It's very important that you do not mistake allergies with your bird having a cold.
If you suspect your cockatiel might have allergies, you might want to develop a checklist to rule out what your cockatiel might be allergic to. Things like a perfume you wear, or a cockatiel food treat can provoke allergies on your cockatiels. What kind of material is the cage cover made of? Certain materials might not be welcome by your cockatiel. Also, when you wash the cage or the cage cover, you might be using a strong detergent that might make your tiel have an allergic reaction.
Also do take a close look at your cockatiel diet. Put your cockatiel on an allergen-free diet (no wheat, no peanuts, no dairy, no chemicals -tap water, preservatives- etc) go over every single thing your cockatiel eats and look at the ingredients (most treats have peanuts or peanut butter or wheat products in them) and put your tiel on a health diet (everything organic, distilled water, no preservatives, etc).