I'm wondering if there are any acoustical panels I can place on my
ceiling and walls to dampen down both ambient apartment sounds, and
intrusive sounds from the outside.
  I already have decent padded carpeting in the room.

Lots of stuff such as acoustic wadding and expanded poly tiles will
absorb high frequency stuff but low frequency is a real problem.
Sheets of lead or rubber are about the best you can do I?m afraid.

Best