It's looks like Corsican mint. Btw, where did you buy it? I've had no luck tracking down Coriscan mint in the city.

I have an indoor mint (not Coriscan) and I've never fertilized it beyond a little bit of compost once a year. Otherwise I water it and leave on the window sill. I'm not sure if you need the light. I was under the impression that Corsican mints don't require a lot of light and prefer dappled light. You need to keep the mint watered as it doesn't like dry conditions.

As for mint rust, not sure. There might not be anything wrong warranting action. Look at the photos on this site, some of the mint leaves look like yours.

https://twogrow.com/2015/04/15/plant-profile-corsican-mint/

I bought it at Chick's Nursery: 8410 New Utrecht Ave, Brooklyn, NY 11214. Last week they still had Corsican in stock, but had moved it outdoors. They rarely have a good variety of indoor plants, and most of their outdoor plants are "boring" species and cultivars, but when they get something weird, it's usually rather cheap. They barely have terra-cotta pots, and don't have a huge selection of small-bags of soil amendments. I assume they do a lot of outdoor and maybe some sort of wholesale.

Those pictures do have a similar reddening... I'll let it go for now, and hope for the best!

I have also been looking for corsican mint. Would like to find it locally but no dice! Lucky you!! Rosie

For posterity, there was something wrong with my mint, I think. I started getting leaves with white stippling on the upper surface, so I started treating with neem oil every four days.

Still don't know if it was rust or mites, (both can look like that, I imagine). But the problem seems to have cleared up/be in remission, as the mint has really taken off!

I've gotten no more red leaves, but I still don't know if they were related to the pale stippling (if they were first stage of rust on this mint) or if they were unrelated.