Must it be raining when the humidity reaches 100%?

A relative humidty measurement of 100% does not necessarily mean that rain is falling. It just means that the air is holding as much moisture as it can at a given temperature, in the form of water vapor, which is an invisible gas.

However, near 100% relative humidity, you can get water vapor condensing into very small water droplets to form clouds, including fog near the surface. Also, the relative humidity at the ground does not have to be 100% to get rainfall. It often happens in the western United States, for instance, that you will have clouds producing rainfall or snowfall which then falls through very dry (low relative humidity) air near the surface and evaporates before it even hits the ground. This is called virga.

-- Michael Bell