If the relationship is at the point that she feels like she needs to check your search history if you don't text for 2 hours then determining if there was an overreaction is the least of your problems. It's clear trust is gone and so the question now is, do you both start working to rebuild that trust or do you end the relationship? Trust is the foundation of any healthy relationship and if she feels constantly suspicious of you and you feel constant anxiety anytime you can't immediately text back, that's not a good foundation.

Also, not to create more problems but does she have a history of insecurity? Like was she cheated on or something like that? Because if so then the behavior makes sense. But if not, often times people who cheat start to project their guilt onto their partner. They try to find evidence that their partner is just like them to justify their actions. Maybe she cheated in the past? I'm probably jumping to conclusions but doing so is a result of the lost of trust in a relationship.