HI,
Just to be clear.
There are three folders called "Library" on a Mac with only the original Admin account. *see fourth Library below.
If you open the Hard Drive to it's top level then you can read Library, System and Users (As well as Applications and anything you have put here.
If you open the System one then there is a Library folder as the next step there.
Also in Users > the name of your Account (Little House icon) then there is one in here.
However since Lion this has been Invisible.
Using the Finder > Go Menu > Go to Folder and entering ~/Library will open a window in that Library
You can also make the Folder Visible on permanent basis if you need to.
Generally Spotlight will not display the results from the ~/Library which is why you will not find it this way.
Fourth Library.
Since Sandboxing came into being the Containers folder has many "Library" folders that apply to each app that can be sandboxed.
Basically all are at the same depth of Containers/Data/App Name/Library.
As you say it is working I would not worry too much about it.
I have just finished installing OS X 10.9.3 and my Users folder seems to be the next one to become Invisible.
8:07 pm Friday; May 16, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad