Last night I took Naproxen about four hours after an advil (ibuprofen). Will I get ill? How will I know? It's for retainer pain.

Retainer pain. Be sure to immediately contact your treating General Dentist or specialist Orthodontist about pain. Retainer may need adjustment. OK to take Naproxin 4hrs after Ibuprofen, but do not take any NSAID for 12 hours after Naproxin .
Should be fine. You should be fine. But it depends on how much Naproxen and Advil (ibuprofen) you took. It it is just one or two tablets of Naproxen or Advil (ibuprofen)'s then it is nothing to be worried about. But if you took large amounts of Naproxen or Advil (ibuprofen) (4-5 tablets each) than there might be some stomach pain, nausea and or vomitting. If this is the case and your experiencing these symptoms then go to an urgent care/er.