Does my boyfriend need to send a text message when he is busy at work?

You could say that. You said you were really busy recently. You must pay attention to your health. Nothing important. Your health must be the most important. I'm really sorry I didn't take care of you by your side. However, the latter is what I want to tell you. I think you'd better not send these messages, because he may be too busy, and these messages may not help him. You sent these messages just to fight and let him. If he doesn't like you so much now, you can find something to do by yourself. There's no need to find him. He will come to talk to you if you can do your own thing well. If he doesn't come, it means there is something wrong with your relationship.