A positive word for someone who is viewed like a sister, but isn’t one
Solution 1:
perhaps you could use "soul-sister" - according to the very trustworthy Urban Dictionary a "soul-sister" is :
"Someone who fully understands you. Like a soulmate, but not someone you want to marry and make babies with. The sister of your soul."
Another option is "sisters by heart". It implies that there is no blood relation between you two, but you're close, like sisters.