White tongue does not equal thrush. Many babies have a white tongue appearance. Thrush in baby is typically seen as white patches on other parts of baby's mouth. If you scratch the white patch and it is red underneath, that is a very strong thrush indicator.
However thrush can certainly be present even if baby has no symptoms. Moms symptoms include breast and/or nipple pain during and in between feedings, (often shooting pain,) itching, red or bright pink nipples, scaly or shiny nipples.
burning after nursing could also be vasospasm. And it could be both thrush and vasospasm.
I am not sure about the milk issue. But here is the kellymom article about it, which is a reliable resource that offers evidence based info. As you can see, even the experts disagree a bit here. http://kellymom.com/bf/concerns/chil...xpressed-milk/
Unfortunately thrush is an incredibly tricky thing, often incorrectly diagnosed (both over and under) and incorrectly treated, and has a tendency to recur, so that-reoccurrence-would be the concern with your stored milk, as carm3 already answered.
This is a good thrush overview https://www.llli.org/faq/thrush.html
and here is one thrush protocol http://www.nbci.ca/index.php?option=...tion&Itemid=17