Yes, "Go in now, the doctor will be with you shortly" is grammatically correct and conveys the same message. However, it sounds slightly more direct than the original version, which uses "Go on in" as a friendlier, more casual phrase. If you're aiming for a friendly tone similar to the nurse's original wording, you could say: "Go ahead and go in, the doctor will be with you shortly." "Feel free to go in, the doctor will be with you shortly." These options soften the instruction while keeping it polite and welcoming. **If the nurse tells you to go in the room, there's not much for you to say besides "ok" or "thank you"**

The nurse can say that instead, yes. But her way was more friendly. Your way is more bossy. And I don't see why you would want to say it. Who are you saying it to? It's for the nurse to say.