In a 68 yr old man who is having acute bronchitis and is using a nebulizer is it normal for his hands to shake real bad, where he can't even write or do anything with his hands?

Trembles is not a symptom or sign of acute bronchitis.

If I were a 68 year old guy I would be asking my doctor what was up. It could be a sign/symptom of anything. Find out what it is.