Trust is a very fragile thing. Once broken, it is very difficult to regain. I have no way of knowing if your girlfriend is being honest about the nature of her relationship with the guy at work. But I do know that the two of you had an understanding about what it means to be faithful and she broke it without talking to you about wanting to renegotiate it. She may be telling the truth that she just wanted to avoid an argument with you. Maybe not.
One of the most important tasks of the teen years is learning how to be in a trusting and loving relationship. At the very least, your girlfriend needs to learn how to approach difficult subjects with the person she loves and not be so afraid of an argument that she hides. You need to learn how to confront a problem directly instead of playing detective.
If we could rewind the tape of life: You would have pressed her for an explanation of her secretive behavior and she would have shared her text messages with you. If those messages were harmless, trust wouldn’t have become an issue and your relationship would have been brought to a deeper level by working through the “rules” of your partnership.
If the two of you can have a deep and honest conversation about how to be trusting and trustworthy, you may be able to salvage this relationship. If the two of you can’t talk this through to the point where you are both comfortable, then it may be best to learn what you can from the experience and to move on.
I wish you well.