Sounds like either the port is damaged and stuck in a contact-mode or maybe you have a software hangup in the music app or dialer/phone app. What steps have you done so far?
Sounds about all you can do without a factory reset, but IDK that Id go that route just yet. Unless someone else can chime in with a better solution I suggest contacting Verizon about a warranty exchange.
You have a 1 year manufacturer warranty. But, I'd have at least the min $3 extended warranty. People get worried about damaged phones and such requiring physical repair and the Asurion warranty, but I have replaced my phone everytime for software issues. Something to think about.