But DD was a little genius and I didn't have a single problem (no soreness, no extra long feeds and she piled on the weight). I bf her for 4 months.
It was hard juggling 2 dc's, so we did have cbeebies on alot while dd was bf.
Once you've got the hang of bf you'll be suprised how little skin you expose. Once you've got the baby latched on your dh could take a photo from the front and all you'll see is the babies head. Nursing vests are good to keep you feeling covered up (and warm!) and a pretty top can go over it and be pulled up when you feed. H&M do good nursing vests, i loved mine.
Expressing and bottle feeding is a lot less discreet than just feeding and would be incredibly hard if you had two children. I know because I couldn't BF ds1 and ended up expressing instead.
DS2 has been a breeze to feed really and DS1 has coped brilliantly (he was 2.3 when his baby brother was born). You can read books and do one handed playing whilst feeding.
I am a self conscious person too and the first 3/4 weeks were hard when out and about because I was not confident. But now we are so good at it that there is nothing to see! You can also use a shawl to cover yourself up if you ever feel shy.
Also remember most public places have breastfeeding rooms you can go to if you prefer privacy. John Lewis and Mothercare tend to be good. If you have a full-length mirror, say in the bedroom, you can do feeds in front of this at home until you are confident nobody could see anything too.
Don't worry about people seeing your body. Once you've got the hang of it you'll be able to do it discreetly. You might need to use a blanket/muslin/cardigan just to cover your tummy up but otherwise no one will be able to tell what you are doing. The other thing you can do is wear 2 tops so you pull the bottom one down and the top one up and baby is in the middle iyswim.