Interesting question. These are aligned for my overall career choice, but have become increasingly less so with my particular job, to the point that I am looking for a new position.
You need to do both. Ultimately, you need to follow your heart and do what will make you feel fulfilled. This requires that you know what you really want out of life. Not just what you are good at, but what is consistent with your values, lifestyle, and inherent nature. You can take advantage of the stability of your present situation to give you the time and space to figure that out, and to gather resources for your future: not just the income you earn, but the job experience, some longevity in one organization, and the good recommendations you can get from your appreciative supervisors. Sometimes you need to do something that isn't right for awhile before you understand what exactly isn't right about it. If only by process of elimination, this will help you identify what is right.
Many young people do face these questions, and if they don't, they often wind up dissatisfied in midlife or their 30's when they finally realize they have gone down the wrong path. Even then they can make a change, but there is often more risk, and more investment potentially lost.
It took me a few years to figure out what I really wanted to do. I sort of knew, but didn't have the confidence to pursue it. I tried a couple other jobs - working in a library, teaching, and finally going into the military - before making the commitment to my long-term career. As for being happy, it is not something I have ever deliberately sought. I find it is a by-product of being able to use and develop my abilities, contributing somehow, being challenged, and generally feeling fulfilled. So, i seek these things instead. Also, there is more to life than work. One thing that helped convince me that I need to change job is that currently my personal sense of fulfillment comes primarily from the things I do outside of work, mostly with volunteer activities and hobbies. This isn't good in the long run, but can tide you over during the time that you are in that stable interim job while figuring out your future.
You might be interested in the experience of Sylvia Pankhurst. She was one of the women campaigning for women's right to vote in England in the early 1900's. While her mother and sister focused on winning over the wealthy and powerful, Sylvia spent her time with the poor women, living in the slums and working in factories to support their children. She had originally wanted to be an artist, saying once that if God had put her on earth to do anything, it was to paint pictures, however great or average her talent. She considered her work with the slum women to be more important and pressing, however, and gave up her dream of art, at least for a time. The moral: there is more than one way to follow your heart.
Suggestion, find something you don't hate and could/can do 'in the meantime', study that, get a job/career going and THEN go from there. Life is like a river though and sometimes you don't know where it's going to take you. Those that can adapt quickly and as often as needed do the best. As a mentor once told me, it's more important to have goals vs. plans, cuz shit happens.
