Can you afford to see her more often? My guess is that if your texting increased after your stress increased it was because you needed her more. I expect that as your stress decreases you will need her less. It is her job after all and you do pay her, so I don't think you need to feel guilty about needing her more right now. And it might be easier to not text between sessions if you see her once a week rather than once a month.

But I can understand wanting to be more independent and not rely on a paid relationship entirely. Will it help to journal and then share it with her? Or to post on this site when you feel like texting her? I think that is what a lot of people use the "Dear Therapist" thread for. You won't be being a pain there, because you know we all "get it". Real life friends can be helpful, but sometimes they can be unhelpful too. So you have to think carefully about who you honor with your trust.