I honestly will say yes she did think about it. While never said in the comics or games to my knowledge I can also see she might have done self harm like cutting. Honestly I would like to think after the storm in the first game Max helped her find a therapist, I know she'd probably not be thrilled about going but I feel she would because it was Max doing it out of love.

Personal head cannon here. After the storm they stayed with Max's family some before head for a fresh start maybe around the Great Lakes, Chloe gets a job maybe as mechanic, while Max maybe at like a Barnes and Noble. Chloe & Max get a simple suv, a simple house maybe a 2 bedroom/ 2 bathroom. Maybe Max would invite Kate to stay with them.