I didn't send a message to each other that day.

I think it's good. If you send him a message, he will check it from time to time, indicating that he keeps you in mind. He is worried that you will send him a message, and he is afraid that you will not find him. If you don't send him a message, you can go about your own business. In fact, the best way to know someone is to ask him directly. You are in direct contact with him, and you can get to know him well by asking.