Anorexic Treatment

I'm 17, I'm 5 "7 and I weight 106 pounds. I began to realize how my thoughts are illogical and I think I might have developed anorexia. Nobody knows what will happen if I went doctor at this kind of weight and was diagnosed with anorexia?

If your weight is still about £ 106 there may be no need to worry. If you're constantly losing weight, then that's another story and you'll need professional help. I have seen many women in your height and weight and even if it is thin, it may not be anorexic.

they put you in therapy and on a meal plan, and probably you diagnose depression as well.

Probably refer you to a psychiatrist and a dietician to help you with meals.

And also, your dr. would control your weight frequently.

You would be given several options depending on the severity, it is. There are specific diagnostic criteria that are required to be met for Anorexia Nervosa, but there are many eating disorders, one of which is "ED NOS" or eating disorder, not otherwise specified.
Your self-assessment of illogical thoughts are a great indicator that you know something is wrong. Please do not delay and seek medical help. Eating disorders become more integrated / difficult as time passes.
Please also do not think you are not "skinny as so and so, you must be" fine. EDS are not to be a certain weight, and they can not be diagnosed by your weight alone.
If the problem is severe, your doctor may suggest an intensive program (google "Renfrew" is a help desk). If it is not there yet, they can suggest counseling or family counseling, individual / group. It may also suggest that she meet with a dietitian to initiate a meal plan.
The only way to know is to try to get help, talk to your parents / guardians of your feelings so they can get things started. Most insurance will cover the treatment, so do not worry about the money, moreover, your health is priority No. 1.