Crying doesn't indicate trauma. You can have trauma and not cry AND you can cry and not have trauma. Plus the method used to try to treat trauma might not work for you. Personally, I would never think it's appropriate to record your story nor do I think you should go over your story daily. That's not how I understand how it works. That could be re-traumatizing and result in flashbacks, freezing, numbness, etc towards your past trauma or even create a new trauma.

Ex-T tried talking to me about my trauma. She knew the basics. We started talking about my mom, and I never cried. Then we talked about my dad... I cried so much. She thought I was faking it. The trauma from each parent affects me differently. I've processed the trauma with my mom a lot and have mostly accepted it. Not with my dad. I still try to see him as a parent even to this day. So I get triggered when any of my trauma comes up with him.

ETA: If you want to know if it's trauma, I think the main question is how it affects your life. I'm sure there's quizzes out there that could help you determine if it's trauma. Just my opinion? Yes, I'd say that could be very traumatic and the fact it still affects your life points to that it's trauma, too.