Bless you, I remember just what this was like, my son really struggled with latch when he was teeny too and the pain reduced me to tears multiple times a day.
I echo what others have said about seeing a lactation consultant; your health visitor should be able to put you in touch with your local infant feeding team but there can be a bit of a wait. If you can afford it I highly recommend finding a private lactation consultant (IBCLC), some will do a video consultation which can be cheaper than in person. I had an in person consultation and within 5 minutes and a slight tweak to my technique I was feeding him painlessly.
In the meantime, for dealing with the sore nipples, the best product I found was Multi Mam nipple compresses. You can get them in Boots. They have a cooling, soothing gel on them and they gave me instant relief. Keep on with the Lansinoh too as it will help stop them getting dry and cracked in the long run, but the compresses were much more helpful for the pain.
While I was waiting to see the lactation consultant I did find that pumping and giving him expressed milk was helpful to give my poor bleeding nipples a bit of a rest. It’s fine to give the odd bottle of formula too if you need a break but make sure you’re expressing if you do that to keep your supply up, if you want to EBF in the long run.
Also check out La Leche League, they have some great guides to positioning and latch.
Well done for persevering, I felt like giving up so many times that first week but last week we made it to 6 months exclusive breastfeeding. If you want to keep going I promise you can do it with the right support and it does get easier! Remember your baby is new at this too, you just need to figure out how to work together to find the right technique for you both. :)