I may be reading this wrong, but it sounds to me like you have your joystick set up fine. Truthfully, I don't remember which axis is X or Y, but when you move the stick left or right the ailerons should move, forward and back will move the elevator.
My interpretation of your problem is that you are not flying with Auto Combat Trim enabled.
Enable it by clicking "options" on your clipboard, then "preferences","flight", and then make sure the Auto Combat Trim box is checked.
Flying with Auto Trim enabled is really the easiest way to go. Especially if your are new to the game.
If you do map your stick to include "manual trim", note that making an adjustment manually will turn off the Auto Trim. Using any of the three "auto-pilot" options will turn your Auto Trim back on, or you can turn it on by toggling it back on with whatever key you have it mapped to, or a button on your joystick if you have one mapped for that.
I personally use Auto Trim for about 95% of my flying, as do most others playing the game. I like to use manual trim while landing, or when I am flying some manuevers. I use some left aileron trim while landing, and trim the elevator, so I can get a hands free descent angle/speed. I also like it when I am damaged, so I can fly back home and land.
Of course, I could be way off regarding your problem and its solution. If you can't get it fixed right away, head to the Training Arena, and look for a Trainer or anyone willing to help get you set up. The problem you have is not "normal", and can be fixed I'm sure. Don't waste too much time trying to figure it out on your own if one of our solutions doesn't work.
MtnMan