What can I do to soothe my nipples during a painful latch?

Lanolin, cool packs. Firstly, work on the latch technique with a goal of a pain-free latch. If it's too late, and your nipples are already abused, apply a few drops of breastmilk after each feeding to moisturize the skin. You can also try lanolin as a soothing agent. Gel-based cool packs can take the sting and burning down a few notches, and a dose of Acetaminophen or Ibuprofen can be in order for moderate pain.
Cracked Nipples. It seems like you have cracked nipples. You could lanolin and its safe for your baby to feed while you have it on. If it does not get better i would buy OTC vit e capsules open them using a pin and apply topically after feeding the baby.