by shuttle cock may be serious if the shuttle cock hits at very high speed. Since you had injury away from the black portion, cornea
you need to worry. Since you didnt had bleeding, it rules out any lacerating injury. If your vision is good you can continue oral pain killers like ibuprofen
, what you are taking now.
However I advice you to visit eye doctor once for examination of the eye including examination of retina
to rule out any damage because of injury .