Hi D.,
Congratulations! I love the Maya slings, they are so great for carrying your baby and keeping them close. As far as covering up during nursing, you may find that just lifting your shirt is sufficient cover and you won't need something over you and the baby. And so what if someone knows you are nursing, as long as you are discreet. Be proud of being a nursing mom. The more often woman nurse in public, the more normal it becomes and it makes it easier for other moms. Try practicing in front of a mirror or a friend and you might find you show very little skin at all. Nursing shirts are great and make it easy to nurse in public. It is going to be summer soon, and a hot cover-up may get too warm.
The slings are so great, I highly recommend one. Congratulations and enjoy your new baby. Don't hesitate to call La Leche League or the hospital lactation consultant if breastfeeding doesn't go smoothly or if you have questions. It can be tricky to start, but is worth it. It shouldn't hurt, some discomfort, but not pain. Call someone if you need help with it. Take care.