Ok, so I completed the helm of winterhold quest and it won't let me start purity of revenge. I waited 30 in game days and nothing. And since finding the problem, I have already defeated alduin and accomplished so much so reloading a save isn't an option. Any ideas?
This quest has significant bugs that can prevent it from ever starting. For your situation in particular, it sounds like you are stuck and won't ever be able to start it on this save:
If Driftshade Refuge has already been cleared, this quest cannot be started normally without a workaround[…] (you will have to revert to a slightly earlier save to do this).
Since you probably cleared Driftshade Refuge during Helm of Winterhold, then only reverting to a previous save or using console commands (on PC only) can make Purity of Revenge start.