How do I know if I just have a head cold with a cough and not walking pneumonia? I don't have a fever. I have a slight sore throat.

Chest x-ray... The only way to diagnose so-called "walking pneumonia" is with a chest x-ray. Symptoms are usually milder and so patients can walk around with it unaware that's what they have. It is usually due to a viral etiology so antibiotics are often not needed or even helpful.
Walking pneumonia. The term "walking" pneumonia applies to a chest infection that is serious but does not make you feel bad enough to stay in bed. It is somewhat difficult to diagnose- -usually when someone has had cough symptoms for over a week and sees a doctor for a chest xray. I assume your symptoms reflect a common cold/sore throat for the first week. After that, get it checked. No harm in waiting unless fever.