Will Aegis of the Gods negate my opponent's Erebos, God of the Dead for me?
Aegis of the Gods will have no effect. You still won't be able to gain life, for the exact reason you suspect. From the definition of Hexproof:


  702.11c "Hexproof" on a player means "You can't be the target of spells or abilities your opponents control."


Since Erebos' ability doesn't say 'target' anywhere, it doesn't target you, and Hexproof has no effect.

Alternately, you can find a way to remove Erebos from the battlefield. Exiling is one way. Erebos can't be destroyed, since Gods have Indestructible. Have you considered cars such as Deicide or Banishing Light?