Hugs lovely.
For everything latch related, look up the Jack Newman website, great videos with expert commentary. Do you think she has pain/tension in her face or head that's preventing her latching? LO1 (and me) benefitted massively from cranio-sacral osteopathy on day 3. He was like a different baby and fed v happily. Breast compressions might also encourage her to work harder.
Can you see an LC thru the hospital if you think you need one?
For your nipples, get multimam compresses - available from boots here. They are amazingly good. Rapid healing and immediately soothing. I would consider a pain killer as well.
The first week can be a bit crazy anyway so one feed at a time is completely the way to go.
For yourself, if you open that sort of thing, some homeopathic camomilla would sooth your nerves, or just rescue remedy if that's easier to get
Sorry that's a bit patchy, have sick 3 to on my knee but HTH. One feed at a time. You can do it.