In answer to your question. Can this spread to your chest? Yes...

However there could be numerous other things so - I am going to list them,

aspiration pneumonia, regular pneumonia, gas (yup!!!!! believe it or not), depending on location it could also be heart issues. So to follow through on the advice of everyone else. Do go see your dr.

Pneumonia can happen silently without you being aware. Aside from the simple fact that you are likely still somewhat immune compromised, your swallowing from the surgery and radiation is likely off. This can lead to small amounts of stuff, getting into places it's not supposed to... namely your lungs.
Pain is always possible with cancer, but if it is big enough to cause pain chances are it was also likely able to be picked up on a scan.
Phone and ask about the scan immediately - this may ease your mind somewhat.

Also you should have had both a chest CT and head and neck. Clarify with your dr. which you've had. (hopefully both) if it was only your head, considering the fact that you are complaining of chest pain, they should set you up for one immediately. and remember it's scary - but it's not always cancer... hugs and take care.