Yes I agree with atat. My T states in his contract that he would not 'friend' any client on social media (he's only on LinkedIn as far as I can tell) and it seems to me that it's essential for healthy therapy to keep personal lives separate.
The mutual friends thing is obviously an added complication that needs managing. It seems important you have a conversation with her about it. It's possible she liked your comment by accident (easy to do with a touch screen! Believe me I have friended people I had no intention of friending! ) but a conversation about boundaries is the best to avoid stress and misunderstandings.