Ok, this is a little silly, but it works. You are:
A personal relationship with God (i.e. YWHW)
(Title) Everyone has and knows one:
From the perspective of the Catholic Church, and most major Christian groups, this is the case. c.f. for example Gaudium et Spes section 1 chapter 1 subsections 14-19
I often create barriers that can be broken.
There's an idea that God tests people and stuff. Like, the book of Job but also in Paul's epistles he talks about ways that a relationship with God necessarily causes you to encounter problems but also you can overcome those problems.
I started as waves but was eventually scratched in stone.
"In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters." So our first relationship between God and the world besides creating is hovering over the waters, which is kind of wave like. Or, better: "And God said, 'Let there be light,' and there was light. God saw that the light was good, and he separated the light from the darkness." --the other traditional 'first' thing God does, and we all know light is a wave (sometimes), so that works too. 'Scratched in stone' works really well also-- we later get the 10 commandments, which are represented as etchings on stone tablets, and form the basis for a different sort of personal relationship with God (as shown by e.g. John 14:15 "If you love me, keep my commandments"). So that's pretty cool.
Now there are thousands of us, none exactly alike.
Well, billions is more than thousands, but it's the same idea. Everyone has their own relationship with the divine, and they're all different.
Communication is key, yet I cannot speak.
Prayer. I mean, 'cannot' is a little strong, but I think burning bush situations aren't exactly common
I know it's not what you were going for, but it fits really well and I think that's really amusing, so there you go ;P