Even if you spit blood without brushing it can still be other things like burst blood vessels. Often there are reasons like coughing, the brushing issue you have found, etc for bits of blood.
Changing your toothbrush for a harder one makes lots of sense. It's like when you start flossing or use an electric toothbrush, they tell you to expect some bleedig from gums until you get used to them. The same with your new brush, adjusting the pressure has sorted it.
So, you found the root cause & a practical solution as well keeping your anxiety down and getting on with you days. Lots to be proud of there!!!
Can you look back and see the difference to where you are now? It can be quite an eye opener when you've turned that corner. Yet back then it felt so hopeless but now you have proof that yes you can do it and get better. So, any little blips, remember this.