Adobe RGB is a document profile .The setting in colour settings is just the default for new documents. You should also have preserve embedded profiles set, so that on opening an existing document the embedded profile is used (whether that be Adobe RGB, sRGB or some other document profile).
The printer profile should be specific to the printer and paper that you are using - so for example I have different profiles for my Epson P5000 printer when I am using Epson Glossy paper or Canson Baryta paper.
Armed with both profiles, Photoshop's colour management system can send the correct values for each pixel to the printer so that it prints correctly.
Select your (accurate) RGB printer profile [for the paper you'll be using] as "device to simulate".
[The ICC profile is guiding the arrow, it'll noit hit the target if its not accurate.]
Set the Rendering intent to the one you'll be using when printing, generally RelCol or Perceptual
You may like to add the "simulate black ink" checkbox as it will, in most cases, by reducing the screen's black intensity, match the (properly illuminated*) print a little better.
The "simulate paper white" checkbox rarely aids softproof accuracy
*The screen should be viewed in subdued light, the proof in bright daylight which menas you cant (in room light) hold up a proof to the screen and expect a match. For that a print viewer lightbooth is needed, or a trip to the window.
I hope this helps
if so, please "like" my reply and if you're OK now, please mark it as "correct", so that others who have similar issues can see the solution
neil barstow, colourmanagement.net :: adobe forum volunteer
[please do not use the reply button on a message within the thread, only use the blue reply button at the top of the page, this maintains the original thread title and chronological order of posts]