Please help me identify the drama where the female lead asked the male lead to hug her tightly and keep asking him to hug tighter until she kinda feels suffocated. I think it has something to do with her needing to leave the male lead??? Thanks

Are you looking for https://mydramalist.com/729363-love-like-the-galaxy-part-2?

In one of the scenes FL is traumatized by bullies in palace and asks ML to hug her. The scene you described happens there.