It does sound a lot like cat flu. It's caused by a virus that the cat will have forever and the condition may come back. Sometimes mild cases require no treatment [there is no specific treatment as it's a virus anyway] but secondary bacterial infections are common.
If the cat is off colour or off it's food or has sticky eyes then you need to go along to the vets. Occasionally it can be serious. Often some antibiotics are what's needed, sometimes just some antibiotic eye ointment.
Things that can help:
1. warming the food [cats rely on smell to eat, so blocked nose = not eating]
2. take the cat in the bathroom when you have a shower [the steam helps clear secretions]
3. use warm water and cotton wool to clean the nose and eyes of discharge a few times a day.
Let me know how you get on.