I can't tell you much more about GarageBand, as I seldom use it.
HOWEVER, I can say something about Y-splitters.
You said you're "..using a y-splitter(L/R RCA to 3.5mm).." But if your mic is a mono mic - which has a cable with only a mono plug on the end - then your Y-splitter is probably picking up sound from that one channel, and delivering it via the 3.5mm plug to
only one channel.
What you need is the
opposite of a Y-splitter: you don't want to "split" the audio from the mic into left and right channels (with one channel carrying something, and the other channel carrying nothing) ..you want to
combine the input from the left and right channels so that the same audio is present on
both channels. (..There is audio on only one of your two, but that will then be fed to
both channels of the 3.5mm output plug, giving you the same sound on both left and right..)
If the quarter-inch plug from the mic looks like this, with just
one separate segment at the end:
..then that single segment at the end needs to be connected to
both segments at the end of the 3.5mm jack-plug ..to feed that single channel of mono sound to
both left and right.
So instead of a connection like this, which takes each of the separate left and right mono signals from mono plugs and feeds them
separately to the left and right channels of a 3.5mm plug..
..you want to connect the mono output of the microphone to
BOTH the left and right channels of the 3.5mm plug. So using the original picture:
..you want to connect together BOTH the little inner red wire (..of the right channel..) and the little inner white wire (..which feeds the left channel..) to the (mono) tip of the mic's quarter-inch jack-plug. You could wrap those thin little red and white wires together, then wrap them around the tip of the big quarter-inch plug (..with the braided 'screen' wires of the little plug wrapped around the metal shank of the big quarter-inch plug..) or you could get a pre-made adaptor which has a single
MONO quarter-inch socket connecting to a
stereo 3.5mm plug.
They're difficult to find, which is why you may have to make your own.
You may need to buy a 3.5mm stereo plug:
..and a quarter-inch MONO socket:
..and open up the socket, connect the 'ground' of the socket to the 'ground' of the 3.5mm mini plug, and connect the 'signal' of the socket to BOTH 'signal' connections in the little stereo plug.
THEN you'll have the connection you need!