We usually diagnose a cold by clinical signs: sneezing, congestion, discharge from the eyes or nose or sometimes fever. If it is truly a cold and caused by a virus, it will usually resolve itself within 10-14 days unless a secondary bacterial infection sets in. A paralyzed larynx can cause changes in voice and sometimes breathing. In some cases it can be very serious. A paralyzed larynx is usually diagnosed by examination of that area under anesthesia. If you have concerns that there is still something going on with your cat, I would talk to your veterinarian. If you are not comfortable with that, I would seek a second opinion.
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My 10 year old, indoor cat has had an extremely cold nose for the last couple of week 
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