If my name is on my mom's bank accounts, car, and house; do I need POA?

That's all good stuff but if mom is competent and willing to grant POA it couldn't hurt to have more arrows in your quiver. It might come in very handy as things progress.

There may be other times that you need a POA. For example, if your mom moves to an assisted living facility, they want either her signature (if she is competent), or a POA signature (if she is not) on a rental agreement.

Make sure you have POA or you cannot talk to utility companies or credit accounts. Get a Health Care Proxy too, when you are with her at the MD's office.