The blackish dis-coloration on eye lid next to your nose is due to the percolation of blood in the sub-cutaneous tissue of the lid which has resulted from the rupture of the stye
. You should continue hot fomentation of the stye. Along with that, take some systemic anti-biotic and anti-inflammatory drugs as well as anti-biotic and anti-inflammatory eye drops locally.
This should improve the condition within 72 hours. However, the blackish discoloration will take time (about 4 weeks) to disappear.