I heard that it is a lot harder to do breast reduction when your breast are shallow / wide root. Is this true?

I think that you have to be seen in person to be properly evaluated.  I will say that narrow based breasts can be difficult to deal with.

I'm sorry to hear about the physical and (possible) psychosocial problems your disproportionately large breasts are causing you. 
It is probable that you are dealing with juvenile breast hypertrophy along with the physical and (possible) psychosocial consequences of this diagnosis. In other words, the breasts are too large for your frame causing  both physical and psychological distress. I am not sure what you mean by “shallow” breasts; certainly, many patients who present for breast reduction surgery have wide breasts and do well with breast reduction surgery.
In my practice, timing of breast reduction surgery is determined on a case-by-case basis. It is NOT too early to do your homework and learn as much as possible  about  breast reduction surgery and the potential risks and complications associated with  the procedure.  I am glad to hear that you have your father's support/understanding.   
As you learn about breast reduction surgery, make sure you read about the potential risks/complications associated with the procedure. You may find the attached link helpful in this regard.  For example, unsatisfactory scarring is  one of the potential complications. Make sure you also understands that further surgery may be necessary in the future (for example if the breasts were to grow in size again).
On the other hand, breast reduction surgery is one of the most patient pleasing operations we perform and I think that for the right teenager (enough symptoms) it may be an excellent option (regardless of the age). Generally speaking, the best I have the procedure performed once you have reached “physical maturity”.
Sometimes breast  reduction surgery is covered through health insurance. The best way to obtain insurance coverage for breast reduction surgery involves some “hoops” to jump through. The more documentation you have (for example, from your primary care doctor, physical therapist, chiropractor etc.) the better when it comes to obtaining insurance “authorization” for the procedure.
This documentation and letter/pictures from your plastic surgeon will help you obtain authorization.
 When the time is right,  seek consultation with well-trained/experienced board-certified plastic surgeons.

I hope this, and the attached link, helps.

I  would have to see photographs of your breasts to tell you of any potential problems with breast reduction, but from your history, I think that you should go forward with surgery. Experienced plastic surgeons are used to making alterations in the incision lines dependent on the individual patient's anatomy.