What is the most likely diagnosis of running nose slight fever and productive cough?

Viral Infection. The most likely cause of a runny nose, cough, and fever is a viral infection. It is possible for these symptoms to be related to a bacterial infection that would require antibiotics, however most physicians will advise to wait 24-48 hours before considering prescribing and antibiotic in the absence of any other definitive symptoms that would suggest a bacterial infection. Hope this helps!