Overview
Cats do not get the human influenza virus (flu), but some are infected with upper respiratory viruses which some term "cat colds". These are generally distinct from the human rhinovirus, or cold virus. Sneezing, nasal (nose) and ocular (eye) discharge may be associated with upper respiratory infections (bacterial, virus, or fungal). These signs can also be due to allergies, foreign material stuck in the nose or in Persian cats (a short-nosed breed) due to the altered conformation of the nasal cavity and tear ducts.
Flu Symptoms in Cats
Wheezing sounds can occur when there is marked irritation or partial obstruction in the nasal cavity, as with inhaled foreign material, or inflammation (as when an irritating compound has been inhaled (e.g., smoke), during infections), or due to abnormal nasal conformation. However, true wheezing involves the lungs. In this latter case, there is bronchoconstriction (narrowed airways) that lead to a whistling lung sound in combination with increased respiration efforts. The most common scenario in cats leading to true wheezing is asthma; associated with airway irritation, or wheezing can occur when something foreign has been inhaled down the windpipe or trachea, or a lung infection is present.
Vomiting is not usually associated with cat "colds", and there are numerous causes of vomiting. In a young, long-haired cat, hairballs can certainly be considered a likely cause. Hairballs can indeed cause vomiting and prior to their usual presentation upon your rug, preceding noises may sound like "wheezing". A vomiting cat can inadvertently get some vomitus into the nasal cavity if the vomiting is severe. The irritation can then lead to secondary sneezing, and nasal discharge.