A power of attorney, which may grant broad or very specific authority, is not something that you need to file for or request from a court. Powers of attorney are routinely drafted by estate planning lawyers. If your mother wants to give you the authority to conduct some or all of her affairs, either now or in the future, you should get her in touch with an estate planning lawyer that can visit with her (and you) about how she may execute the required documents.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should not rely on this answer alone and nothing in these communications creates an attorney-client relationship.
It's also important to realize that there are two types of power of attorney - general durable powers of attorney, which are for handling financial and property matters, and health care powers of attorney. Your mother should have both.