Take a look at this - it's about 'nipple vasospasm' - and see if you think it fits your experiences -
www.thewomens.org.au/Nipplevasospasm
I had similar pains very badly in early pregnancy (along with the slightly alarming 'traffic light' nipple colour changes). It really is the 'cigarette lighter' feeling someone else described, and I find it very hard to sit still or concentrate on anything once they've kicked off!
The main advice seems to be to keep them warm, and not let them get cold in the 1st place. Which is all very well, but I didn't seem to be very good at it (getting out of a heated car into the cold was a particular 'trap'. And getting out of the shower.)
What I did in the end was get some of those self heating stick on pads - Curaheat do them, in Boots etc - for period pain and back pain etc, and then stick one on my clothes at the front, so I had a constant portable 'hot water bottle' to carry around with me.
It lasts all day and works very well, although a bit of clothing disguise is necessary (I stuck mine on a vest top underneath another top, and then smothered neck and chest with a large scarf). Otherwise it looks a bit like you have a sanitary towel stuck on your chest...
Hot water bottles were good at home, but no use for work or out and about, obviously.
Sounds a bit 'mad lady', I know, but it was a huge help in December/January. At 20 weeks, it seems to have got a lot better - although I note SardineJam is still suffering, so I'm wondering if BF-ing is going to be another Nipples of Fire experience. Hmm.