The headaches were just a way for Halima to mess with Egwene's mental state (tiredness/bad sleep, concentration etc.) and to get a motive to sleep near Egwene to be able to interfere with her Dreams.

It's all there in Aran'gar's POV: her skills with Dreams/TAR were limited, so she needed to be very close. To be very close while Egwene slept, she needed a reason for Egwene to ask her to sleep nearby, and that reason was the headaches Aran'gar created and that she posed as having the skills to help with. Once again, that's a confirmation that Aran'gar didn't use Compulsion on Egwene: she had to manipulate her the mundane way, she had no "magical" influence over Egwene that succesful compulsion would have given her. Halima may well have been forwarned Moghedien taught Egwene about Compulsion, the weave and how it worked. Add to that her strong will, that probably made it very dangerous to attempt - Egwene's inconscious would recognize and resist that weave with all her being.

When the headaches still didn't give her enough time near Egwene, she increased them and killed two of her maids, who among their daily tasks, were helping Egwene from supper to sleeptime, and sleeping on a cot nearby. They rotated. What happened after their deaths was that Chesa served Egwene all day, and often at night Halima offered to take over, soothe her headaches than do the maid duties to put her to sleep (there are many people very suspicious of Chesa now that Sheriam, who provided her, is confirmed as BA. Though some think all there was there was that Sheriam tried to use Chesa as spy on Egwene without Chesa being a DF, and as Halima used Sheriam as spy she left Sheriam's spy alone...) But Egwene has kept her distances to the end, she liked Halima but found her nosy (and never forgot she was also the secretary of a Sitter).

I find that in the end, most people with big Compulsion theories simply don't understand well how Egwene reasons and formed her opinions. Most of Egwene's thinking about Rand for instance comes from how she reacted to what happened from Tear to Egwene's departure for Salidar: eg: Moiraine suddenly acting like his servant and Rand playing the ruler often with arrogance, how things have gone between Egwene and Rand after Moiraine's departure, the dealings between Rand and the WO, Rand's arrogance with Tower envoys, the fact the Rebel embassy suddenly went out of contact, Rand's efforts to find out where the Rebels were, the fact he believed Alviarin would help him, his sending of Mat to Salidar and so on. Then there came all sort of distorted news/interpretations, like the apparent compulsion of AS in Cairhien (which did happen. Egwene simply mistook what Verin did for something Rand did), and the fears he had acquired an Aes Sedai advisor Siuan always thought was a DF.

At first, Egwene did want to deal with Rand on a more personal level, reason with him directly (and bring him on the side of the rebels). Siuan convinced her she couldn't possibly do this, politically. It's Siuan who is the most fearful and circumspect about Rand, she convinced Egwene to put any notion of dealing with Rand herself out of her head.

Egwene's change of mind about the Oaths? It's Siuan again. Egwene explicitely said so herself.

The Seanchan? Egwene's opinions come from a traumatic personal experience as damane. She's been their slave. She didn't manage to convince the Aes Sedai, all of them from Siuan to Lelaine to even the sisters in the Tower didn't see any way the Seanchan could ever get close without them knowing it weeks in advance as their armies moved... so they dithered, and rejected Egwene's dreams. Egwene stepped out of a Dream once that was showing her how to solve the conflict. She refused to see it to the end because it involved her and a Seanchan woman "helping each other". That's nothing to do with Compulsion, Egwene hates the Seanchan bitterly since Toman's Head.