I have never seen 18mm tires. Get a metric ruler and pump the tires to 100 psi. Use the metric ruler to measure the full width side to side. I seriously doubt your tires are less than 21mm wide.
Have your neighborhood bike shop fit your new tires to make sure they are suitable for your rims. Most road bike rims work very well with 25mm tires (most 25mm tires have a MEASURED with of 23mm or 24mm) and 25mm tires are a good choice for a rider under 200 pounds who rides on smooth roads.
If you weigh more than 200 pounds and ride on dirt, gravel, or rough pavement, 28mm tires would be better, if your bike shop thinks they are a good match for the rims.