My girlfriend told me that you don't have to send me text messages every day when you are tired. What does that mean? Am I interrupting her?

You didn't bother her, but made her feel that you didn't care enough about her. You send messages just to perfuse her, or she is testing you, to see if you will really stop sending messages to her in the future and test your position in your heart. At this time, you should care more about her, take care of her and protect your feelings. Women are sensitive animals.