I am certain that you’re not the first person who has googled their therapist. Many therapists advertise and have profiles on the Internet, and they do this precisely because they know that people are researching them. It’s not unusual to want to research a potential therapist.
You may be overreacting to what you have done. It’s highly unlikely that she knew that you were looking at her account. She likely made it private for some other reason. Perhaps it was related to professionalism. She might have realized that having a public account might be problematic in her work as a counselor. There are thousands of potential reasons why she made it private. In all likelihood, it probably had nothing to do with you.
Yes, you should go back to therapy. You and she had a good connection and you should not let this get in the way. In addition, you stated that therapy is an important part of your life. That would suggest she was having a positive benefit for you. Ending the relationship over this minor occurrence would be an unnecessary loss.
Finally, I would encourage you to talk to her about what happened. In all likelihood, this will be a nonevent. Please take care.
Dr. Kristina Randle