I'd say,
of course you are scared to cry since you've been holding back the tears for so long.. And something did happen that made you start to bottle up your emotions, something that was
very real to your five-year-old self even if you can't remember what that was..
All I can say is, it's not wrong to cry. I feel I'm probably not the right person to give advice as I have the exact same problem of not being able to/wanting to cry in front of others.. But I also have awareness and know that the reason I think it's embarrassing is because no one listened to me when I cried as a kid - I might even have been punished for crying, I can't remember. Whatever it was, I know the
other people were wrong, and I was right. We're
right to cry, it's just a reaction to certain things, and energy that needs to flow. It's just that we need people who are willing/able to listen, who won't break when we cry, to truly learn it's OK to cry. I completely understand your fear and feeling awkward about it - because at one point, it wasn't accepted

I really feel for you!
Seeing the counsellor sounds like a fantastic idea to me! I can only speak for myself, but I've felt really safe talking to a therapist. It's their job, they've chosen to do it and are paid to listen! Any counsellor worth their salt won't laugh at you, punish you, nor hurt you in any way for crying, or for showing any emotion for that matter.. You might even start by telling him you're afraid you'll start crying and that you feel it'd be embarrassing! I'm sure he'll tell you it's OK, it's normal, he won't mind.. And you can go on from there.
You know, I actually had a friend whose father was an alcoholic, and she kept most of her emotions about it to herself until she started seeing a counsellor as a teenager. She told me that on her first visit, all she could say was, 'I feel so bad' before she broke into tears. And then they went on from there. It was OK
The best of luck to you!

It'll be alright!