I will disagree kindly with most of the responses here related to you doing something about the pain that seems to imply your feelings are unjustified.

Your husband from your descriptions is carrying on far more than he is letting on. The truth is, that no man that is devoted to his wife will 1. carry on with another woman and share pet names, personal details that he would normally share with his wife (dreams, etc) if there is nothing going on. He's full of crap that there is nothing there. I'm sorry but very few people give pet names to people that they are not somehow very attached and fond of. That's a truth I hate to give you but I think you may be trying to deny something that is very obvious to me.

2. would carry on further with the woman after having been found out and acting like it's all the woman's fault for continuing to pursue. You've looked at the conversations that followed, does it really look like he's trying to avoid or push her away? You never really said what was in those texts that followed, so I ask you to honestly look at it and evaluate whether it seems like he's trying to change the relationship as he said or if it seems like he's continuing the same culture of conversation with her.

Please take a step back from beating yourself up for being a crazy jealous wife and realize that you have justified feelings for something that is clearly wrong and is a betrayal of you, your trust and your marriage.

To be completely honest, if he were trying hard to make amends and win your trust back or make sure you know it's nothing, he would be instantly cutting her off from these conversations. His bs as if it's her pursuing is completely untrue, it's not really difficult to shun behavior from someone when you're committed to just that. he doesn't seem to take this seriously and is playing you for a fool.

Honestly it's not your feelings that need changing, it's your husband and his very possibly cheating ways. even if not a physical cheating, he is, without a doubt, having an emotional affair with this woman and it NEEDS TO STOP.