As others have already said, you should probably be fine with just a heater shirt, but everybody is different. Given that you have mostly been free skiing, let me also add that course skiing is quite different from free skiing. With free skiing, even if the water is cold, you don't stay much in it: you do your deep water start and then you are just more dependent on the air temp than on anything else. With course skiing, on the other hand, you spend much more time in the water than above it: you start, one pass is over in 20-25 seconds and you drop back in the water and you wait (for the boat to come around, for your coach to give you comments, etc.). If the water is cold, it gets to you quite quickly.
Have fun! I'm envious!