Hi OP. I had very similar latching problems with my now 5 week old DS. I only stuck it out until day 4 and that was hell so you are doing way better than me for a start!
The difference in my experience was that DS wasn't really feeding at all when he was on the breast and was probably starving hungry during his first few days at home. We got to the bottom of this after seeing a lactation consultant on day 5.
I tried all sorts from support groups and You Tube to nipple guards and special cushions. It sounds like nipple guards might help you, Boots sell them for about £5. There is also a type of cushion which is sort of circular and clips round your waist; it's called My Breast Friend, they are £55 in John Lewis and are a lot firmer than the traditional v-shaped pillow most people use meaning the baby is in a much straighter position and you are more comfortable as a result.
It was actually the nipple guards that made our problem apparent. They are clear and the lactation consultant said that the end should have been full on milk when DS was feeding. All I could see was condensation-like moisture on the inside and I had to squint to see that.
I made the decision to express and give this via a bottle, topped up with formula at night. It wasn't what I hoped for and I desperately wanted to breastfeed but it has worked out really well for us. DS is still getting 80% of his feeds from me, he sleeps for long periods during the day and only wakes once at night. I'm no longer in agony, still have my sanity and others can feed him to give me a break. Midwife is really happy with weight gain despite the tricky start and DS weighed 10lb 2oz when we were discharged at 2 weeks - although he was big at 9lb 5.5oz when he was born!
There are obviously down sides as with anything. It can be really difficult to make sure you regularly express throughout the day. You need to do it 6-8 times a day and once at night when the milk producing hormones are at their strongest. I've also shelled out over £200 on a medela double pump and dr browns bottles, although you could get cheaper alternatives if you wanted to.
Breastmilk can be out of the fridge for up to 6hrs so we tend to use this during the day when we tend to be out and about. It can be stored at the back of the fridge for several days, although you'd have to check how many days because it never lasts long enough in this house with guzzling DS forme to know! You can freeze it as well.
I am an absolute advocate for breastfeeding and it sounds as though you have every reason to continue if you want to. People say these early weeks are extremely hard until things just click and then you'll look back in a few months and be so glad you stuck to it. However I just want you to know that there is an alternative if you decide it's not for you and you shouldn't feel like you have no other options.
Good luck and well done 