Is it true that if she filed for her citizenship, she can petition for me by filling out n-600 form where I will automatically become a citizen?

You can only automatically become a US citizen if you have already been a permanent resident. If you are not a permanent resident yet, then your mother would have to petition you for permanent residence once she is a US citizen.

If you live with your mother, and she becomes a citizen before you turn 18, you will become a U.S. citizen at the same moment. Even if her naturalization happens a little bit later, you might still get the citizenship because the law extends the deadline by the length of time her naturalization application will be in processing. But your mom should file the application without delay: if you miss the deadline by a day, it will take years and a very difficult process to make you legal.

You can become an automatic US citizen on the basis of your mother's naturalization if you have a green card and are physically living in the custody of your mother. Otherwise, your mother can petition for you on form I-130 and you can concurrently apply for adjustment of status on form I-485 when she becomes a US citizen. Both forms must be filed with USCIS before your 21st birthday.