Hi, I have played the Highland pipes since I was ten years old, and can remember becoming dizzy when I first started, especially when I started on tunes on the practice chanter, and tried to play for a complete part. Maybe if you just play the chanter for a shorter time, ie, stop for breaths more often, until you build up the technique or capacity for longer blows.Even now I find a long session on the practice chanter harder work than a session on the pipes. A couple of points to remember. To make it easier for yourself later on, do not allow your cheeks to blow out, I have seen more problems through players not getting a seal around the mouthpiece because of this, than possibly any other single cause. When the cheeks expand it seems to detract from the lips gripping the blowpipe. Having said that, I have seen a few pipers play with puffed out cheeks, but not many. Another helpfull idea may be to go to pipe band contests or recitals and watch how pipers blow. Top bands have a complete lack of movement amongst the pipers, they stand stock still and play. Basically if your pipes are set up right,and you are comfortable with them, there is no need for any movement of shoulders, or huge arm movements. One last thing, try to blow from your diaphragm, not from your chest. I find blowing a really hard set of pipes gives me a dull ache around the lower back , just below the ribcage. If your shoulders are pumping up and down as you play, you may need to improve your technique. Much of this is in the future for you, but I believe that correct blowing is as important as any other technique you have to learn. Without this you will not blow tone, or keep a constant sound.
Keep it up, I hope you get as much enjoyment from the instrument as I have had for the last 38 years.
Cheers, mcpiper