I struggle with attempting to cry as well. My mom said similar things. "Don't cry. Stop crying. I can't understand you when you are crying" When what she should have said was "Go ahead and cry. I might cry with you, but you cry until you can talk. Then we will talk and cry more if we need it."
As a result I need to be completely alone when I need to cry. I have to be somewhere that I know I won't be interrupted or heard or seen.
The only people that have seen me cry is my husband and my therapist. And I won't cry in front of my husband. I feel guilty every time I do. Like it's manipulation or something. My therapist is different. I need to be real in therapy or it won't work. He sees the crying but its the me still trying to hold it together crying so I can pay attention to what he is trying to tell me.
There's some rolling hills behind my house with some trees. I go out there and do the ugly crying. The really, really bad crying. I start journaling and I get to the point that the emotions are welling up. And because no one is around I feel like it's ok to hurt. It's ok to cry. No one can to see. I'm real in my journaling. Rambling spelling errors. Crossing things out. Incomplete thoughts. All of it. there are so many tears in my journal.
I don't know if you have access to a place that you could be alone and uninterrupted, but those are my suggestions. And if you can't cry remember it's ok too. Don't put too much pressure on yourself.