Conjunctivitis or Pink eye sometimes lingers as mild redness and discomfort with a foreign body sensation that takes a while to disappear. Constant fishing out of the discharge that collects at the medial canthus of the eye near the nose bridge is probably causing the redness at that location in your case. Firstly refrain from doing that as it turns into a vicious cycle. The more you dig, the more it collects. The fact that the discharge still exists means you need some medication to clear the remaining effects of infection. Start an antiinflammatory eye drop preparation like Ketorolac eye drops used 3 times a day for 7 to 10 days in that eye. Use refresh tears eye drops that are lubricating medications to clear any residual gunk that may accumulate. All should be better by the end of the course that usually is around a week.