Alison, it's ok to get dizzy... I think everyone does at first. I'm not sure why it only happens when you're standing up though (note to self: try playing pc standing up later!). What everyone's said about taking a breath sooner than you think you need to is good advice.

I found the main problem I had at first with the pc was sore/numb lips and cheeks from maintaining a good seal round the mouthpiece. This is something that gets much better with time though. I wish someone had told me when I first started that biting the mouthpiece makes it harder to seal. Eventually I worked out that the most comfortable position (for me!) is with the mouthpiece sort of resting on the front of my teeth and lips "kissing" the end of it.

Here's a really good piping forum where I have learnt many useful things. :-)