I haven't told my T the actual lengths that I've researched her (and I have gone a little too far imho too).
LinkedIn I personally don't think is such a bad thing. It's not really a personal site, but a professional site.
My T knows I've done extensive research. I admit to knowing the information I found if she finally tells me about it. She does ask how I find all the information. I dodge the question, but do explain that I'm not paying for any services or doing anything illegal. She actually gets shocked now when she finds out I don't know something about her

She even expected that I saw her facebook page (which I hadn't at that time, so I went home and found it

).
Like you, I know where my T lives...basically. I would never go there. I figure, if I don't want her showing up at my house, she definitely doesn't want me showing up at hera. I also understand how that would be disrespectful to her. I do have a fear of seeing people in public. I told my T I won't even use the restroom in her building for fear of seeing her outside the office. Plus I don't drive...
My T has actually asked me to use my researching skills on others... she just recently told me to research a possible DBT therapist.
I have stopped researching my T. The only thing I look for are new pictures of her. The rest I want to learn from her.
Least you know you're not alone in the researching. And if it's definitely bothering you, you should bring it up. You didn't do it to harm your T. You just wanted to know more about him.
I hope everything goes well!