You can consider nursing your baby while he/she is in a baby carrier: http://livingwithlowmilksupply.com/10-tips-for-breastfeeding-in-a-baby-carrier It sounds like a great skill to acquire because not only does it sound discreet and convenient, you can do it both outside and at home. Not sure if it's a solution you will be keen on, but thought to share. :)
You can practise and build up to it gradually. Start off nursing in a designated nursing room with a nursing cover and slowly build up to it. Invest in a good and secure nursing cover -- it will be your best friend especially if you're shy about these things.
Keep in your mind that breatfeeding is your baby's right. No one could stop you for doing that. When you realise that it's not a mum's obligation but something you do naturally, i believe the comfort will come itself.