There is a big difference between being a stalker, and committing stalkerish actions! Its clear from your OP that you don't have it in you to be the kind of scary stalker everyone fears.

I do speak from experience. Being stalked is the scariest thing I have ever experienced. I suspect most therapists have also had to deal with clients whose morals are not as high as yours, and who have no restraint when it comes to attachment and stalking. For all they know - you could be one of 'them'.

I really strongly hope that you do speak to your T about this. And Im saying that for her sake, as well as yours. My 'evil' stalker never spoke about, never acknowledged, we never ever verbalised what he was doing to me. Its terrifying - because you don't know how scared to be. You don't know just what that person is capable of. Speaking about it outloud. Being honest with her about what you did and why - Im sure she will understand your motivations, and feel so much less threatened by you having the bravery to bring this up. I imagine any distress you caused (if she saw you) would dissipate once the two of you spoke openly about your need for contact. Once she understands your motivations she will realise you are not the kind of person she needs to worry about.

Your actions are completely understandable. I hope you are brave enough to talk about it, and that your T is understanding and helpful and the two of you can move forward.