Katkins,
Just a quick suggestion for helping ease the embarrassment. Buy one of those crop top type bras (even a size too big) to relax in as they are quite comfortable and put the breastfeeding pads inside to soak up the "spills". The crop top bra will also be useful to sleep in when you have had the baby 'cos sometimes you may feel like you need some "support".

At least if you are planning to b/feed you can look on the bright side and know you will have lots of milk!!! lol. A bit of a pain tho' if you were planning to bottle feed.
Don't be embarrassed - remember thats what bbs were made for!!