Rabbits can suffer from sneezing, runny nose, and runny eyes, but fortunately, your bunny cannot contract a human cold, as the viruses that cause such misery in humans are not contagious to rabbits.
The condition commonly called "snuffles” in rabbits, is an infection of the upper respiratory tract that can result in sneezing, runny nose and eyes that is caused not by a virus but by bacteria. This disease is very contagious and can also affect the eyes, ears, and other organs. If diagnosed early it can be treated, but it can become chronic or fatal if left untreated.
If your rabbit is sneezing or shows signs of discharge from the nose and eyes, especially if such discharge is whitish and thickened, she needs to be seen by a veterinarian. The vet will have a sample of nasal discharge taken and sent to a laboratory for culture and sensitivity testing. Once your vet receives the results of the test, they will be able to prescribe the particular antibiotic(s) that should be safest and most effective for your rabbit's infection.
Runny eyes or nose, labored breathing or chronic sneezing can also indicate allergies, a blocked tearduct or other problems and you should see your vet. If you can’t get to the vet yet, in the meantime you can flush your rabbit’s eyes and nose with sterile saline and use artificial tears to keep their eyes more comfortable. Use warm compresses to remove crusts from around your bunny’s eyes and nose and keep them clean.
Keep an eye on your bunny’s behaviour as a change can indicate an illness. If they are usually excited to see you when you come home, but are acting lethargic or otherwise not their usual selves, you should get it to a vet soon. The sooner you catch an allergy or infection the better as rabbits can go downhill fast when sick. Noticing illness in your rabbit early can save you a lot of money as well as hard work and heartache.
Observe your beloved rabbit's behavior, activity level and droppings each day. Each rabbit is different and knowing what normal behaviour is for your rabbit could save their life.