Mistake 1: Forward current 20 mA. 20 mA is just what is often used by LED manufacturers to specify some characteristics. But it is not the current one needs to operate an LED at. There should be a diagram in the LED datasheets of every self-respeciting LED manufacturer, showing relative luminous intensity over forward current. You'll notice the diagram doesn't just have a single dot at 20 mA, but shows quiet a range.
Mistake 2: Forward voltage 1,85 V. Forward voltage is not fixed. It is a function of forward current (if you drive the LED with current). Or you can also say forward current is a function of forward voltage (if you (try to) drive with a constant voltage).
So let's pick some realistic values. Lets say you want to drive the LED with 5 mA. You find in the datasheet that its forward voltage at 5 mA is approx. 1.5 V. So you need a resistor of approx. (3.3 V - 1.5 V) / 5 mA = 360 ?. Hu, pretty close to the 330 ? you found :-)
But there is a problem. With that 360 ? resistor the LED wouldn't run at exactly 5 mA. LEDs come with some manufacturing tolerance and temperature sensitivity. The forward voltage over forward current function varies widely. So the above procedure, picking the forward voltage out of the diagram for a given forward current and then using that to calculate the resistor, is a rough approximation only.
What that 360 ? (or 330 ?) resistor ensures is that the current can never exceed 9 mA (10 mA respectively). And that's how you usually dimension such resistors. Decide what current you don't want to exceed. The 330 ? engineers apparently decided 10 mA is a nice value (and it is). 10 mA = 3.3 V / 330 ?. Then you let the non-linear system (the diode makes it one), find itself an operating point within that absolute limit. Because that's good enough for the purpose.