Paramore is definitely a huge influence on me.
Their entire latest album, After Laughter, is very relevant to mental health.. in fact it was the first album since the captain, Hayley Williams, got Anxiety. "26" especially is really heartwarming and simultaneously heartwrenching LOL. On the previous, self-titled, album, there is a song called "Hate to See Your Heart Break", and that is oddly comforting too. I swear, someone should make an hour-long loop of the outro to that song.
There's also really intensely uplifting songs, like Breath of Life by Florence and the Machine, Shake It Out by Florence and the Machine and Fight Song by Rachel Platten.
I guess it depends on what you're going through. Some of my favourite breakup songs are Torn by Natalie Imbruglia, Since You've Been Gone by Kelly Clarkson and Gravity by Sara Bareilles (the Little Voice album version.)
There are also some love songs.. most love songs break my heart, but there are some that really emulate the kind of love I want to give. The 2006 ARIA Awards version of Watch Over Me is [...] amazing. I want to learn how to sing, and sing that at my wedding if that ever happens. It's a trio with Kasey Chambers, Clare Bowditch and Powderfinger captain Bernard Fanning. Another love song I really appreciate is Who'd Have Known by Lily Allen, it is so simple and comfortable.
I could talk a fair bit about this, but I'll stop LOL. Good luck :).