To me it sounds like a deep platonic relationship, but maybe I am biased because: Most women where I am from would act this way with there best friend, no-matter their gender or any parties sexual orientation. I went to a left-wing nerd high school where groups of mix-gendered friends would hold hands with each other pretty regularly. I also used to have a very close platonic guy friend whom I trusted a lot and we would even spoon, when we had to share a bed some nights. He always respected my queerness and boundaries, until he got a bi-sexual girlfriend who forced herself onto me a few times when she got drunk. He tried to capitalize on these events a when they happened, due to me not literally throwing her off of me each time it happened. I tell you this as it was one of the things that ultimately broke my trust with him, so my bias is saying that you shouldn't make a move if you want to keep on being friends.

That being said. If your feeling for her are affecting your love life or it is making it difficult for you to be friends with her you should absolutely tell her how you feel. Just make it clear that, because of your background things like holding hands etc. feel very flirty to you. That you want to keep respecting her, but that in order to do that she needs to tone down physical platonic affection because for you those are actions are reserved for people you date. Try to focus on how things make you feel and repeat the fact that you understand this is not what she is intending to do to you. This helps make sure the other person feel reassured that you are not blaming or accusing them of something they aren't 100% responsible for.