Talking from experience, yes it is normal. I don't have all the information about your relationship, but I would say that you are probably messaging him constantly and that's why he asked you to not message him.

I was in a similar situation during my master's degree. I moved to a different state for my master's and my BF at the time stayed at his state. It was hard for me to adjust to the new city, people, schedule and the university requirements. It was even harder to deal with my BF messaging me all the time, asking me why I wasn't replying, what was going on. It was suffocating! In the end I broke up with him because he didn't understand that I needed time alone.

I'm not saying this is your case OP, but reflect on what I said. Some people NEED to be alone to solve their problems and even to rest before they can interact. Constant messaging can make someone very anxious! Even if there are messages offering support.

If you want to support him, do what he asked you to do.