I had this problem last year and also this year. Both times resulted me paying out for a new steering rack, as the rack was leaking fluid.
Like you, the steering rack started to whine when turning the wheel either to the left or right.
First port of call would be to check your PAS fluid.
VW charged me around £1100 all in last year and this price included wheel alignment (£99)
This year, I went somewhere else, but still cost me over £600 incl new front tie rod ends and wheel alignment.