Try some different comfortable positions. Yes your nipples can very much be sore. I suggest you use Google for some breastfeeding positions and images of properly latched newborns. I think imagery wold be more useful then attempting to explain.
I had trouble nursing with my first baby. Ouch, is all I can say. At one point, on day three of being home, he had blood coming out of his mouth. What was that blood? Oh, just his latching on incorrectly causing me to have cuts. Like for real, it was that bad. I was about to give up completely at that point but my darling husband went and called Le Leche league to talk to me. I about killed him for that as I didn't really feel like talking to those who were going to tell me to NEVER give up . . . but in the end, they DID help. Lanolin was my best friend (purple tube, ointment you put on the nipple), they told me to air dry, that helped. And I just worked on proper mouth placement. Eventually he got it. Now, I did supplement with formula at that time and he then, for thereafter, nursed AND took bottles of formula. I liked this though because then my husband could feed baby and I got a break here and there. My second exclusively nursed and I felt like the family cow tethered to baby day and night. LOL (doesn't that sound glamorous--- it actually was a wonderful experience but a lot of responsibility to be the only food source for your baby!). Anyway, they have lactation specialists as well. Call your pediatrician and ask for advice. But start up of nursing can be worrisome and frustrating. And then it can get all better. so, hang in there.
My OB's office had an older midwife and when I was having trouble they had me come in early and she privately have me tips with baby at the office. I liked that I already knew her so it wasn't a totally stranger.
I had a nurse at the hospital tell me it was 'toe curling pain' - ouch! I kept some lanolin on hand when my kids were first born and then I got used to it and did fine. I even invested in some gel pads I found at Target -they could be kept in the fridge and felt amazing!
With the latch, I had issues with that too. I have what is called an 'inverted nipple' and it caused some complications. They have nipple shields which help some people, I found it awkward to use. I did meet with a lactation consultant at the hospital where my son was born and that helped a ton. She was able to help me with the latch and be more comfortable with nursing.
Hope this helps! Best of luck!