Look at your behavior and ask yourself what you want? It sounds like you are unsure of yourself and your ability to be "good enough" for someone else. Your girlfriend has the "right" to talk to whomever she wishes to in her life, she has a past and may have a future with/without you, that can't be known right now.

Right now, when you are with her, you could be enjoying her and your life but, instead, you are making yourself unhappy concentrating on what she may/may not be doing in her own life. Look at where your focus is, on her. You cannot make yourself happy (and you're the only one who can because you are the only one who can "know" you completely) by giving someone else your focus and attention that you should be giving to yourself and how to make yourself happy. Do you enjoy being jealous? Do you enjoy the time it takes to drive by her house and looking at the website (sounds kind of boring to me)? It is not about her, it is about you.

It is not whether she is trustworthy or not, is cheating or not, if you get your "excitement" hoping to catch her and prove yourself right, that would be about you and what you were wanting to do. You are in control of your actions, driving by her house is about you. If you love her, I would decide you want to give her joy, would try to think of ways I could comfort or cheer her and be there for her, support her in her depression? Instead, you are looking for ways to show yourself you are "right" not to trust her.