All fillers last a long time in the undereye area because it is not a highly dynamic area. Currently, the best fillers for that area are Volbella®/Restylane®Silk/Belotero®. Please consult a board certified aesthetic dermatologist for a consultation.
Sorry to see that your first experience with lip fillers has been challenging. Rest assured that injection induced bruises heal completely on their own with time. However, there are many things that can be done to heal them faster.
1. Use warm compresses- 3-5 minutes 3-5 times per day...
This lump above the lip is not a vein. It is Juvederm which has been misplace. I see this sometimes as I am injecting that there is a channel that the fillers spreads to during injection. I can easily be dissolved with hyaluronidase. You might try massage to the area but it probably won't work.