you're only eligible for an 18+ Oyster card, to get a 16+ one you have to be at college doing A levels etc.
without an Oyster card it costs about £2.30 each way to get from Denmark Hill to London Bridge or Blackfriars (depends which campus you're based at), so assuming you make this journey at least twice a day, it will be cheaper for you to get a zones 1-2 travelcard on your Oyster.
a weekly travelcard costs £16.90 or a monthly one costs £64.90... this will cover all National Rail journeys you make from Denmark Hill or anywhere in zones 1-2, plus all tube journeys within zones 1-2, and bus journeys in all London zones.