Hi baked potato - sorry to hear you are in a lot of pain with b/f...
Does DS have entire nipple and area around it in his mouth when he feeds? If not, he might be sucking on the nipple only, which will make you v sore. If the latch is wrong, not only will it make you sore, but baby might not gain as much b/c he won't be getting the full amount of milk...
Unless your baby is losing weight, I wouldn't worry too much about your supply; I fed twins and could rarely express more than 1-3 oz at a time. Some women just express more easily than others. When you feel comfortable enough, could try feeding DS while expressing from other breast... it is an awkward position, but could help you express more in less time, as baby brings on the milk flow.
I don't know what your BFC has advised about using b/f shields, but mine told me not to use them more than a day at a time; she felt they would make the nipples more sore. When I had one of my nipples crack and bleed, her advise was to air out my breast - literally - and I went without a bra for a day. In terms of support it felt strange but it actually helped. I kept feeding though that day was really painful; the next day the pain had subsided and was nearly gone the day after that. The nipple cracking I experienced was due to expressing too vigorously; wasn't poor little hungry DS2's fault - all down to a hungry machine!!
Keeping b/f pads clean and dry if you use washable ones is also important, so your nipples don't get chafed by the dampness.
I hope I've mentioned something that will be helpful, and that I haven't said anything to contradict your BFC or bring more confusion to the emotional ups and downs you are already experiencing!
You've done really well to get to 3 weeks if you have been sore all the time; most people seem to give up quite quickly. For myself, I found that the "emotional hump" seemed to be somewhere around 4-5 weeks; it was as if I suddenly felt confident that the twins were getting enough, and most of the soreness and strangeness of b/f had worn off.
Maybe it is down to the drop in pregnancy hormones that we seem to struggle through the first month... in other (non-western) cultures, women within the family structure rally around mothers with newborns to provide practical and emotional help after a birth. I think we miss out on some of that.