Latching

I'm a first time mom and just had my baby girl about 3 days ago. I've been trying really hard to breastfeed but because the shape of my nipple, it makes it difficult for my little one to latch. The nipple isn't really defined, more of a cone shape at the end. They fill with milk and make it even more difficult to breastfeed. My daughter can't really open her mouth wide enough to latch on. For the time being, I've been just pumping the milk and I give it to her that way. I worked with lacatation consultations at the hospital who recommended a nipple shield. I tried it but because of the all the milk that is produced, it doesn't stay on. I've also been trying nipple stimulation to help form the nipple but no results so far. I'm just looking for tips or advice to help my baby latch. I've never experienced this, so I'll take any advice I can get.