hi there, the white discharge at the edge of the eye is because of conjunctivitis
and the swelling is also because of the same. The haemorrhage or blood that you are seeing near the cornea
could be due to conjunctivits and if you have been prescribed any eye drop
please continue using them in the prescribed manner. The haemorrhage should subside on its own when the conjuntivitis is cured. If it continues even after that then you should visit an opthalmologist and get an opinion on the same,.Take care.