I wasn't familiar with the Sturt's Desert Pea so had to look up that one. Very interesting bloom and such a gorgeous color!
Do you have any trays/bowls of pebbles and water to raise humidity? That's what I always used in CA when I had conditions such as yours and still use here in the winter for some of the indoor plants. It can get so dry when it's cold and the heat pump is running a lot.
Mint is definitely a thirsty one! But I love it. I hope I haven't lost too many this winter. They are in containers outside.