Just wanted to add my support and urge you to get out and about. Some great practical advice in this thread, and once you've got your clothing sorted, the best thing you can do to increase your confidence is do it!
With my first son, I was self conscious at first, so I'd feed in special bf rooms when out, or in the car, and even with in-laws I'd go and sit in the conservatory and feed. Then one day, when he was about a month old, I sat in the cold conservatory listening to the laughter and conversation going on in the next room and thought 'sod this', and bit the bullet. If you have the vest/loose top combo no one can see anything (I've been at parties and had people walk past me feeding standing up and they've stroked baby's cheek, as they didn't realise I was doing anything other than having a cuddle)
Believe me, it's much more pleasant if you're out and about to grab a magazine/book, cup of coffee and feed in a coffee shop than in a smell loo (especially if you're talking of feeding half and hour plus sometimes). It definitely gets easier very quickly, and I promise you I never had any comments or even funny looks (bf eldest for 9 months, 2nd son for 13, so lots of public occasions. Feel a bit cheated actually, had my answers at the ready in case anyone tried!)
My size varied between 36-40 d/dd/e, so not talking little boobs (although sadly a different story when not pg or bf!)
Good luck and enjoy - it's actually quite liberating! x