Is being am orthodontist a job for people who may be shy? If it's not a good fit, what careers in the dentistry field might better suit me?

I was always a shy person, especially at your age. As I got older, I "came out of my shell" a bit, but I've always been an introverted person. It is certainly a challenge to remain shy when you are in a people-oriented profession like dentistry. I've had to work on my people skills quite a bit. I'm not saying that one can't be shy and be a dentist (which one must become before becoming an orthodontist). I'm merely saying that shy people may have more of a challenge than people who are very outgoing. In my years as a clinic instructor, I've noticed that outgoing students seem to do much better at reaching their goals earlier in dental school than the more quiet types. That's a broad generalization and there are some students for whom that isn't true, but I still think it's harder for us shy people. If you decide that it's really the career for you, I'll bet you get less and less shy about it.

I can agree with the advice Dr. Pinney has offered above. I would wonder exactly what you mean by "shy". There are people who are nervous meeting new people. There are other people who may well have more serious problems interacting with people. Difficulties of that magnitude will pose obstacles in many professions.
For the purposes of this conversation I'll assume you are garden variety shy--say, meeting someone on a first date, going for a job interview, etc. It is very normal to feel shy or anxious in these situations,but these are also skills you learn by going through them again and again. They DO get easier with practice.
I was painfully shy in some social situations--including (when I first started) meeting new patients. I have to smile now--I saw my first real live patient in dental school on my 22nd birthday. I was so self-conscious that this very sweet middle-aged lady, who KNEW she was my first patient--actually comforted me and told me how well I was doing. Needless to say, this was above and beyond what I should ever expect from a patient; but also she was aware that she was being treated in a dental school, and would be treated by someone without years of experience.
It took a long time--years actually, before I became fully comfortable in my professional skin, but I started doing better almost immediately, and knew that even if I found these interactions stressful that things would get better with time.
Orthodontia is not very different in this regard from most other clinical dentistry, except that (as with pediatric dentistry) the bulk of your patients (certainly not all) will be children; which means not only are you going to need to be able to manage kids (who may be fearful) but also manage their parents (which is another thing altogether). These too are learned skills.
There are some areas of research and perhaps oral path and public health that may not require quite as much public interaction on a daily basis. They may be less stressful for those with crippling anxiety. But if you do have anxiety of that magnitude, it's another issue completely, and should be dealt with appropriately with another professional.

But normal shyness? I wouldn't let it discourage you from the orthodontic field at this stage--even wallflowers like me eventually get more comfortable