How can I let my mom monitor my bank account without letting her touch my money?

Just give her a copy of your monthly statement with the account number deleted 

No need for POA

You are an adult, unless there is a court order giving her guardianship due to your diminished mental capacity she has no right to monitor your finances

I'm not entirely sure what you mean by 'monitoring'.

If you mean just letting mum know what you have spent each month, then that is easy. Just show her the statement each month.

The real question is why does your mother feel the need or right to monitor your bank account when you are 19 years old?

If you're living at home (or in college with her support), then that might be a condition of the living situation.

My suggestion - you don't give her access to your accounts.  Your bank should have an option to export transactions records from your online banking to an external file such as a .pdf .csv (which can be opened in Microsoft excel) or directly into an accounting software program such as Quickbooks.

Pick a format that works for you and create a folder on a computer or a cloud based drive (if you don't share a home computer).

Once each week you can log in to online banking and export your transaction records and save the file in that folder where you mother can access the report. But don't give her your password for online banking and don't put her name on your account.

This will allow her to see your transactions, but she will not have access to your money.

It should only take a few minutes to log in and export the file

You are confused about a POA, it will mean she can have control over your money and you don't want that do you?

How old are you? It makes a difference.

Re your Update. At 19 you are a grown up, you tell her No, or you print out a statement for her to read.

Are you an adult?  You simply say "no".

If you are a children, you have no other option for her to have full access since you will have a custodial account.

And power of attorney gives her full rights to the account.

Online access?  No.

Print access?  Ask the financial institution to do a duplicate mailing to her address and tell her she can open the mail and read it.  The only thing she can do at that point is talk to you.

POA?  No.   Every bank I've ever worked with demands the POA to use their form without alterations, which means you pretty much can not only look at the account, but she can sign checks and remove all of your money.

You misunderstood something. Do not give her a power of  attorney till you totally understand it.