To answer your question, Yes. I advise that running away is not the solution. Maybe you should consider counseling, including possibly having your mother participate in group or individual sessions to try getting to the core of the issues you and your mother are having.
If you are under the age of majority, 18, and you commit a delinquent offense then you will could be charged with a crime in juvenile court. If you run away, your mother can call the department of juvenile justice or police and report you as a runaway and unruly which means that you could end up with charges against you and potentially end up on probation. If you are close to 18, you should try to work things out through counseling or some other means. If you just turned 17 and you are self-sufficient, you may file for emancipation. However, you should research this further to determine if you would meet the criteria. Some information can be found at: http://www.georgialegalaid.org/resource/emancipation-of-minors.