I would rather say "Feel like criying" instead of "Want to cry". According to the Cambridge dictionary "want" means: to wish for a particular thing or plan of action. In my opinion, you don´t really wish to cry or plan to cry. In the other hand "Feel like" means: to seem to be something, or (esp. of weather) to seem likely to do something. Examples: I felt like a fool when I couldn’t remember her name. She said she didn’t feel like herself today. It feels like rain.
Onurkan Simsek 3340