Honestly, as a woman...I would just say it straight out if it was something that made me uncomfortable.
I mean...why give you the runaround if I wanted to make sure you knew all I wanted was to be good friends. Linking arms to me is part of the lost act of chivalry. Same as walking someone to their door, etc.
Would you be brave enough to write her a letter just summing your feelings?
Or perhaps just let it be for a bit and if she’s disconnected from the friendship you have with her, tell her. What ever it is.
Hope all the best for you,
Jen