So my mom has power of attorney, durable power attorney and medical. Can she stop me from moving out and living my life?

Hissy, under what circumstances did your Mother become your POA? This is something, usually, that is conferred on a person by the person requesting it. That is that you would have signed a document asking your Mom to to take over for you to help you. What was the reason that was done?
We need more information.
Also, with medical power of attorney she is there to help you and she is privy to your medical information.
If you have not been judged incompetent you can remove the POA for both any time you wish.
Generally when a parent needs to be in full care of a child who is now an adult, to have access for taking in assets and paying costs of living and bills, to take one medical information and care, that is a guardianship appointed by a court for a child unable to manage his or her own health or finances.
Can you tell us a bit more of what is going on with your life?

How old you are and the reason why you assigned Mom as your POA would help in our answers. Were you unable to care for yourself so Mom held POA to handle you finances and medical? Meaning, it was temporary till you could handle things?

POAs are assigned. They do not give someone the power to keep you from moving out IF you are able to take care of yourself. Can you work, can u pay bills and afford a place of your own? Really need more info.

POAs can be revoked. You can always assign someone else.

Possibly, yes; but I wouldn't expect she wants to. Stop you living your life, that is. I can quite imagine she'd want to stop you moving out unless she has complete confidence in where you're moving to.

But what's the trouble?

If the documents are for mom to have them for you you can change them any time if you are considered competent.

Your mom has those documents for you Hissy?
How old are you and mom?
How did she come to have those documents for you, if that is the case?