As it stands, you are at least a few years away from even entering a counseling program. These programs are selective and you're going to need to several recommendation letters and a resume with relevant research, volunteer, or work experience to be competitive. They also usually have prerequisite undergraduate coursework in psychology, statistics, and basic sciences. You're likely going to have to work anyway and, by the point you are ready to apply, you will have built up at least a couple years worth of work experience and be on better professional footing. Psychotherapy as a profession is not a something you can realistically look into as an escape from working in an office setting.

As for having more freedom or the freedom to drop clients, this is not something that one does lightly. Clients are sometimes suicidal or in danger of hurting others or themselves, after all. The fact is ALL people who walk into a therapist's office have the potential to be unpleasant sometimes. Most are perfectly kind and polite people, but everyone has their stories about difficult sessions or clients. Likewise, the mental health community comes with its fair share of egos as well, and, depending on your initial setting, you will start your career with much less freedom than you will as a starting employee in the tech industry.

I'm not saying these things to dissuade you. But the best candidates for this work know full well that mental health is some of the most difficult and thankless work, and are fully prepared for it to suck (at least for the first several years). It seems like you're looking into being a therapist to get away from certain unpleasant things about your present industry, but the truth is, mental health is probably going to be more frustrating and more demanding than the complaints you have about the tech industry. This is something to keep in mind.