I've already completed Amren's, but she still won't give me the quest. Any suggestions?

I'm not getting that quest from her this time either. The speech option just isn't coming up.

Do you have Amren's quest to retrieve his family sword in your journal? If so then Shahvee won't offer her quest until Amren's is completed.

No. It's not in my journal at all.

I have found success by always doing Shahvee first. But - that doesn't help you any right now, eh - the way the radiant quests work is that the first time the NPC spawns for you (even if you don't see them/interact with them), they are assigned the destination for their radiant quest. If that destination is already assigned to another quest/NPC, you won't trigger their quest. Meaning, the dungeon Shahvee wants to send you to is already spoken for. It is either in an active quest in your journal, or it has been "taken" by an NPC that you haven't even gotten a radiant quest from yet (you spawned them when you entered their cell, they got the script for their radiant quest, but you haven't spoken to them to trigger their quest), or it is in a dungeon that needs to respawn before it will trigger.
Solution: wait. Do other radiant quests, clear up your quest log. Try her again. Wait again. And remember, cleared dungeons take 30 days to respawn.

That fits completely with the way I've been playing my current game. I've been going all over and talking to everyone and I have a very full quest journal. I got Scouts-Many-Marshes quest in Windhelm for the first time ever and I've already done Amren in Whiterun. I'll get more quests done before I try talking to Shahvee again. Thanks for that.