TLDR: I love mathematics but can't find a way to study/do research without becoming unhealthily obsessive. Any tips on how not to think about mathematics all the time, on how to manage intrusive thoughts?
Background: Three years ago I graduated with a Master's in pure maths & theoretical computer science from a top school in the UK. My grad thesis had applications in machine learning and led to 3-4 papers accepted to top conferences in that field. I loved every bit of it and could 'easily' have moved on to a phd, but decided to take a break.
My brain is somewhat obsessive by nature, and my last year at university was filled with thinking about problems regardless of my desire to do so. I generally seek to have a balanced lifestyle (friends family sports arts etc) and this is more important to me than excelling only at one thing (maths), but my brain would not let go of me. It became difficult not to think of problems in my free time, especially when trying to fall asleep (insomnia & waking up in the middle of the night to write solutions to problems). I still managed to keep a balanced lifestyle, but my life was sporadically permeated by obsessive thoughts about mathematical problems.
Post-math: At that point, I decided to stop maths for a bit. I worked for a year and then got a semi-random opportunity to go to a professional dance school for a couple years, which I recently finished. I'm still obsessive, but I've become somewhat less agitated in the brain and developed deeper connections to other people and to my own body/emotions. I'm 26 now. I could become a full-time dancer and might do that for a couple years, but it's not much of a long-term project. I'm still highly drawn to mathematics and could probably get back into it, whether phd or industry internships... But I'm afraid of my brain.
The question: Can I become a professional mathematician without becoming overly obsessive/compulsive/unable-to-control-my-thoughts? Do you have any tips on how to manage an obsessive/always-thinking mind? Would doing research in industry make for a better work-life separation than academia?
EDIT: Thank you so much for your thoughtful replies and good intentions. Their many flavours helped me get a sense of the many ways I could deal with my problem, and how there was hope in turning it from a curse to a blessing. I got in touch with a public mental health institution and hope to see a therapist in the coming months (long waiting list!).