Ok. Take a look at this link:
On the 6 page is says the requirements for you to acquire U.S. Citizenship at birth, that your mother had to live in the U.S. at least 10 years before you were born and that at least 5 of those years were after she turned 14. It's going to be close because you said she lived from 14 to 19. You will need to prove ALL of those years. If you can only prove to 18, you won't be approved.
As to how to get an approval, it's either filing the N-600 or the N-600K. Here are links to both:
Please read the instructions carefully. For the N-600, it says you should not file this form if you ae the child of a U.S. Citizen that regular resides outside of the U.S., but for the N-600K, it says you should not file the form if you are a child that has already acquired U.S. Citizenship automatically under section 301, etc. which I think you have. So it's probably the N-600. If you are not living in the U.S. at this time, you may have to skip the N-600 and apply directly or a U.S. Passport proving that your mother is a U.S. Citizen, that she lived the time in the U.S. before you were born and that your parents were married at the time of your birth.
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