Consider rephrasing your question so that it is less specific to you personally. That benefits others struggling with similar questions:
As I read it, you're on a path of self-discovery and you have recently concluded that your current direction (phd in a theoretical, mathematically oriented field) doesn't meet one or several of yours needs (you mention a desire for meaningful interpersonal interactions).
I want to impress on you that it takes a lot of work and self-discovery to figure out what type of role, organisation and what activities make a job enjoyable to you. Allocating some thinking time (a few beers in the sun, a couple of long walks or showers) to it helps you make good decisions in the near term, but you need both positive and negative experiences to really figure it out. It usually takes years and multiple jobs. It can be sped up, but not hurried.
Optimizing your net happiness
Personally, I try to approach this as a mathematical function that I want to maximize, with enough inputs that the search space might as well be infinite. Changing too many variables at once is a random jump in the search space - it might work out, it might not. Controlled changes not only improve my net happiness more often than not, they also teach me about the topology of the rewards space, thus increasing the probability that my next set of decisions results in a further improvement.
So I document the process. I keep pro/con lists for projects I've done. I keep wishlists, of what I'd like to see and do in future roles. Given that job titles are used differently by different companies, I advise you to create a list of properties of different job roles and companies that interest you. I use that to explain my motivations in job interviews. A clear and well reasoned motivation has helped me get a number of jobs I wasn't (yet) qualified to do, thereby optimizing that reward function more effectively.
Using your interest in psychology as an example
Lets consider your dream job as a psychologist as a vehicle for self-reflection. Get as specific as possible about the things that your current field lacks and the desirable aspects of the psychology field. This requires that you answer:
What type of psychologist would you want to be? What sort of capacity - therapy, diagnosis, advisory. Are you looking for an applied role, or would you like to develop and trial new treatment approaches? What sort of interactions do you want to have with your patients - and what patient group would you like to work with? What type of organisation - structure, culture, team composition, responsibilities? What is the probability that you can get into that sort of role - and what would the time-line be?
It is essential that you go pretty deep with this! Consider the interactions with 15-25 y/o clients that suffer from anxiety and/or depression. Compare that to geriatric patients suffering from dementia. How do interactions vary between a diagnostic setting, versus in-patient and out-patient treatment? You may have to deal with a group of patients where you make little to no progress with many clients. How does that impact your sense of enjoyment, achievement or success? Can you predict that based on past experience?
Tying it back to your current field
Your recent Msc has taught you a number of skills that can be applied to many different job fields. For one, I can promise you that you've invested many more hours in your mathematical background than most people in a humanities, business or medical field. You also have specific knowledge you'll never use again - but the process of studying subjects such as String Theory has prepared your brain to quickly grasp key properties of problems from all kinds of fields.
You also have a number of innate skills and proclivities. Maybe a desire to help people. Or to solve problems cooperatively. Or an interest in types of work that not all mathematicians and physicists care about. You might be more people-oriented than some of your peers.
If we just take 'MSc in math-heavy field' and 'demonstrably a people person', some roles where that could be a benefit (that come to mind because I've considered those roles) are:
- Sales engineer: Translator between non-technical customers and a company's engineers.
- Scientific programmer: Helping less-technical researchers with the development of complex simulations or the implementation of computer tasks for psychological research.
- Programmer or analist at an NGO, or other firm that creates value to society.
- Data Scientist or image-processing software developer at a company that develops hardware for radiation therapy and medical imaging.
- Trainer, coach or mentor: Virtually every technical role in a large company can be augmented with these responsibilities, often it's a requirement for senior roles.
- Scrum Master, Product Owner, Management roles: To be excellent in those roles, you need to enjoy figuring out what makes the people around you tick and how you can maximize that potential. Whether it's about steering the business, dealing with resistance or identifying talent and empowering it.
- Transitioning to a job or PHD in Human-Computer Interaction, Applied Cognitive Psychology or AI for decision support systems is absolutely possible with your background.
- You might enjoy a PHD with a focus on Science Communication or STEM education.
You could start by looking for alumni of degree programmes relating to your MSc on LinkedIn or Facebook. Use yearbooks, if you have any. Message people that have ended up in interesting roles or at interesting places. Many people love to talk about why they like their job.
