Hi Kiera, It is so honorable that you enjoy helping people alleviate their suffering; I have spent my entire working life in the field of mental health and I find it very rewarding. Let me answer your question in sections: First, it is not necessary to go to medical school to be a psychologist. Medical school is the pathway to psychiatry but not psychology. In order to become a psychologist you will pursue a Doctoral degree; either a PhD (which is a research style degree) or a PsyD (which is an applied degree); but neither require medical school. You could also consider a degree in Counseling, which is a Masters Degree. Counseling allows you to provide therapy for clients but does not allow you to perform psychometric testing like a Doctoral degree does. Some people do not enjoy testing and assessment, and want to strictly provide therapy, counseling is a good fit for these people.
Once degreed, and in pursuit of starting a practice, you would need to become paneled with insurance companies if you would like to charge people via their insurance (some clinicians have cash only practices and do not bill insurance), rent a space, get some furniture…and start advertising. Having a private practice is a fairly easy process to start-up but much more challenging to maintain. Reputation, networking and advertising are key strategies to success…being good at what you do is also important as most in this field build business via referrals.
If you are serious, willing to invest time and energy, and are competent, it is possible to be quite successful in the world of private practice.