So I meet this girl and come to find out that my great uncle is her great uncle..? So this means her grandma's brother married my grandma's sister! So does this mean were related?. ahhh!

That means that you are paper cousins. You are not related through blood, just marriage.

From your title, I am going to assume you like her. I personally wouldn't go for it.

You could be related through inlaws more so than blood line so you would have to check the exact relationship in the family tree for each of you for direct bloodline.

At any rate you would be more like second cousin
Second Cousins are the people in your family who have the same great-grandparents as you. but not the same grandparents.