I think Headspace can definitely help you with that. Do you have a community mental health team? That is where I was able to get a case manager alongside my psychologist and psychiatrist. Linking with them sounds like a great idea. Sorry to hear about your confusing experience with your GP and the psychiatrist. Whilst the psychiatrist had a point about expertise it was unfair of him to scold you. My experience with Headspace had been majorly positive and I hope the same for you. Maybe you can debrief with the professional they link you with about your conflicting experience and they can offer so more support and advice.
I wish you the best in your recovery journey and so proud of you for taking the first steps 💜