A sense of urgency is a fairly common symptom in people with generalized anxiety disorder (GAD). The disorder is characterized by many different types of worry in many different types of contexts. To be diagnosed with GAD, a person should have a number of symptoms and the feelings would have to interfere with function to some extent.
If the feeling exists on its own, it cannot be related to GAD. It could just be an anxiety focused on where you are going or trying to avoid a certain episode of being late.
In order to get to the bottom of this feeling and to cope with it, it is important to follow the path. In other words, find out when and where you feel that sense of urgency.
Is it on the way to work, shopping, meeting one of your family members, etc.? When you've pinpointed the moment when you feel anxious and rushed, challenge your thought process.