I can run but not walk. Wherever I go, thought follows close behind. What am I?

Why this works

This riddle plays with the double meaning of the word "run." In one sense, it refers to a nose "running" when it produces mucus, often due to a cold or allergies. In the other sense, "thought follows close behind" cleverly suggests that when someone is experiencing a runny nose, they are often preoccupied with their thoughts about their discomfort or the need for tissues. Thus, the answer "your nose" cleverly ties together these two concepts!