Your situation seems to be a fairly common one for people who are fascinated by how our minds work, but also trained or educated in basic sciences.
A few things come to my mind that you should be aware of - I don't see them as pro's or con's but at least can help you compare:
1. To be a psychiatrist - after college you'll do 4 years of med-school and then 4 years of residency. To be a clinical psychologist, I'm guessing it is a 4 year program for a PhD or a PsyD and then another year for internship, but I'm really not sure. I'll ask one of the psychologists here and give more info later. My own sense is that medical school is much more time intensive and much more stressful, however, you receive markedly more diverse training - physiology, anatomy, pathology (you've already done the biochemistry stuff) as well as rotations in internal medicine, ob-gyn, surgery, neurology, pediatrics, etc. You certainly don't need this experience to be a good therapist, and much of it you probably don't need to be a good psychiatrist (I hope the ACGME isn't reading this

) The PhD clinical psych programs will give you more focused education on psychological theory, neuropsychological testing, and theories and practice of therapy (this is again my guess as I've not done a clinical psychology PhD program). During a residency in psychiatry, you can certainly get exposure and education in all of these areas, and you will definitely get some education in these areas if you didn't want it. The difference would be that you'd want to choose a residency program with good faculty in the areas that interest you. The vast majority of time spent in residency is working with patients, and most of the education comes from supervisors telling you what they know regarding the particular things you see, as well as reading research articles and book sections on the areas of interest as they come up.
So that's some info on the educational component, and talking about 5-8 years of your life is a significant amount of time.
2. The practice of psychology and psychiatry is quite different. See my other posts in this forum about differences between psychology and psychiatry in real practice. I know many psychiatrists who are excellent therapists, and I know a few psychologists who are terrible therapists. If you are smart and motivated and have some basic interpersonal skills, then with a good training program you can be a good therapist either from a psychiatry residency program or a clinical psychology program. I do know some psychologists who are very interested in biology and they understand that much of many types of mental illnesses are rooted in biology. Being able to discuss this with their patients is often critical to optimum treatment.
Overall, based on what you describe, you seem like you would find psychiatry more interesting than becoming a psychologist.
My main question is, if you have always had a passion to go to medical school, what has prevented you from applying and doing that already? You are probably already aware that medical school can be very difficult to get accepted into.
Let me know if you have further questions.