My girlfriend snooped through my phone while I was driving

While I was driving, my girlfriend was using my phone to call her mom (her phone was dead). My girlfriend was using the gps to get to our destination while talking to her mom on speaker, I look over at my phone to see the next direction and low and behold I see her going through my messages! When I looked over she was scrolling through a conversation and quickly turned the phone away. She said, "I got stuck in your messages and couldn't get back to the gps, it just randomly went to your messages screen." I made it clear I didn't believe her, she has an iPhone too and knows how they work… We only talked a little bit about this incident and I had nothing to hide on my phone anyways, but where should I go from here? I don't think there's any validity to her "doesn't know how my phone works" story.

If you got nothing to hide, don't worry about it.

Maybe you should have a talk with her about trust, clearly there's some trust issues between you two. It maybe nothing, I know it's a common thing for couples to become paranoid and snoop through phones. My girlfriend and I both don't know each other's passwords to things like social media accounts because we trust each other and value each other's privacy.

Tell her to respect your privacy. Doesn't mean that you guys are in a relationship that you have to share everything. Unless you did something that warrants a check in the messages then she should stay out of it. The same thing goes for you too.

You get a car charger for the car and when her phone dies in the future hand it to her.

You caught her in a lie, don't worry about it, you know she lied, she knows she lied.
Put a password on your phone or an app lock on all your apps, this will keep them from opening by accident and locking your co-pilot in the messaging apps.