Could be a mild upper respiratory infection (URI), which appears during times of stress (a new home would be a stressful situation). The majority of cats carry one of more of the viruses that cause URI symptoms (herpes and calici virus being the most common). Maintaining a strong immune system by feeding the best diet you can (ie: NOT kibble) is one way to help. When symptoms do appear, you can add 500mg of L-lysine to the food once or twice a day. If nasal congestion increases, try some steam therapy several times a day: run a hot shower for 10 mins while you and your cat hang out in the bathroom. Antibiotics are usually useless in treating URIs unless there is a secondary infection, sometimes indicated by green goopy discharge from the nose or eyes.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler