Hey there Jesse M.,
Thanks for reaching out to Apple Support Communities. We understand Notes is opening automatically as soon as you unlock your iPhone. We’ll be happy to help.
When it opens, does it seem to open to a specific note or anything like that?
If you haven’t already, force close Notes and then restart your iPhone using the steps in the following links. This can often resolve issues like this:
How to force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone
Make sure your iPhone is up to date as well:
Update your iPhone, iPad, or iPod touch
We hope this helps.
Take care.