You have my sympathy - I had similar probs, compounded by an allergic reaction to the brand of nipple cream I was using.
If the pain continues after you have finished a feed, then I suspect your nurse is right. If it is thrush, the bad news is that according to my midwife and GP, there is no systemic anti-fungal licensed in the UK for breast feeding mums, although there is something that is unlicensed that some GP's apparently will prescribe. My GP gave me canesten to use externally on my nipples, which you have to wipe off before feeding, but I did not find it made much difference. When the pain started lasting from one feed to the next and I was in tears during feeds, I gave up and put dd on formula. She seems happy enough, and I no longer dread feeding her.
I was really sad to stop breast feeding, and it took me about two weeks to come to terms with that was what I was going to do - during that time I was expressing milk and bottle feeding dd at most feeds, as that was less painful for me, and for some reason the pain didn't last as long after feeds when I expressed. I have to say, that now feed times are enjoyable and always followed with a good long cuddle, whereas before they were an ordeal, ending with me not wanting to hold dd because it HURT! I also suspect I was not letting her feed as long as she wanted.
The La Leche league website has got some useful info under the heading 'Yeast', but their information archives are US based, and it seems that there are drugs licensed there that are not licensed in the UK. Another US website with useful info is breastfeedingonline.com
Your midwife and/or health visitor may be able to help with the diagnosis as well and offer suggestions on how to deal with it - my MW was not averse to ringing my GP and telling her what to prescribe!
I hope you find a solution that works for you. Best wishes.