Go back and ask to see another GP. Not his/her place to judge your degree of discomfort, or to refuse treatment. 'Not that bad'? Who the hell do they think they are?
I had a similar experience, I have to say - the first doctor I saw looked terribly sympathetically at me and said 'yes, these early days are so hard, aren't they' and asked if my mum could come round to take the baby out for a walk in the pram to give me a break. Clearly that would be very helpful in treating a yeast infection...
Then when I asked for another appointment with a different doctor, they had to go out on call and I was sent back to the first useless one who still wouldn't prescribe. Third appointment I got someone sensible and straightforward who prescribed fluconazole plus everything else, and it was cleared up within a week.
So it really is worth persevering - please do try again, and don't feel embarrassed about keeping on going back to them.
Other things that can help:
wash everything that comes in contact with either of your skins in a proper hot wash
probiotics (acidophilus) and grapefruit seed extract as supplements for you
cut out sugar as much as you can (hard I know when you're feeling tired and hungry, but if you boost your protein intake it can help with cravings)
calendula cream for the baby's bottom can be helpful
If the worst comes to the worst and you can't get the doctor to prescribe, I would just get someone to go and buy over the counter fluconazole for you and not let on that it's for a breastfeeding mother. You are NOT going to do your baby any harm by it, and at the very least, if you get some relief it will be diagnostically useful.
Grr. It makes me so cross that people are still having such difficulty with this issue - I reckon it must be one of the biggest causes of people unwillingly giving up breastfeeding before they want to, and it would be so simple to issue clear guidance for GPs that would eliminate the problem completely.
Good luck, and do keep us posted about how you're getting on.