Gosh, no, your period isn't going to affect your ability to breastfeed at all.
SOME women don't ovulate until they wean completely, whereas others start really quickly.
SOME women find that their milk drops for a few days before their period but picks up again quickly and this is overcome by feeding more frequently. Many women find no effect at all.
SOME women find that their nipples get a bit sore just before their period. Others don't find any changes at all.
Have you looked into safe contraception while breastfeeding? The mini pill, for instance, is ok, but not the combined pill.
Some other things that flag at me though:
Are you feeling generally low or just with AF maybe returning? Have you spoken to your health visitor about post natal depression?
Has the tongue tie been snipped? If your baby is struggling to open her mouth properly it may seem that it's "small" but may be the TT. If it's snipped you might want to see if it's re-grown.
A month of Fluconazole is a long time. Have you got a review appointment with your GP? Thrush is utterly miserable and if that's still the problem it really needs another look at. It may be that it's not thrush though, and is compression pain from a poor latch which can feel similar to the stabbing pain that you can get with thrush.
There's a lot going on here love, and I would really urge you to talk to someone in person. Maybe your health visitor if she's good with breastfeeding. Certainly a breastfeeding line such as NCT or LLL, or maybe BfN.
You've worked so hard and you CAN do this.