Lucy....I have this too, I've never heard of anyone else with this! It IS Raynauds of the Nipple, and it's basically when the capillaries seize up and direct blood flow away from the nipple, that's why the end of the nipple goes white. Haven't had my baby yet but I've been anticipating problems with bf because of this. Listen, if you still have milk coming in it might not be too late to get baby back to bf.
I've had this since I was 12, and I find that it is brought on by cold (doesn't have to be freezing outside, I had an attack last night walking from the house to the car parked directly outside in the rain) but in my case it can also be brought on if I think about it too much. I get it in the middle of the night when I'm asleep too, but it can be soothed, there's no need to suffer.
First off, the only thing that will ease it is heat. Now I've tried everything from hot baths, compresses, heat pads, hot water bottles, the hairdryer, even getting dp to suck them to try and get the blood flowing. (This sounds silly if you don't have this condition but honestly, it's like a combination of cramp and being stabbed by a hot pin, it's VERY painful)
The best thing is dry heat for example a hot water bottle, heated rice bag thingy (you know, the cushions filled with rice or wheat that you heat in the microwave for a minute) or the gentle heat from a hairdryer. It's very easy to damage your nipples trying to warm them up with something that's too hot. In desperation I've even dipped them in very hot water before now. Don't do it, it makes them sore.
These days I carry a small panda pops style plastic bottle with me as it's easy to refill with hot water from the tap and hold against you in an emergency. I'm sure there are more sophisticated options out there but the one thing you can almost guarantee is that wherever you go you will be able to get your hands on some hot water.
As for the breastfeeding thing, I've heard that drinking tea before bf is good as it has a natural ingredient in it which opens capillaries. Obviously also doing it in a warm room and keeping a hot water bottle nearby is advisable. Warm heat with a hairdryer after baby is finished to dry the nipple is a good idea, as leaving it damp will start it off.
You might have to work a bit harder, be a bit more careful, and have a bit less freedom than other mothers, but I do think it's possible to bf with raynauds. I certainly intend to and mine's pretty bad.
Fingers crossed you shouldn't suffer with it through summer too as it'll be hot, so now would be a great time to give bf another go if you can bear to. Good luck with it!