My baby accidentally ate honey. He is 10 months old. How worried should I be about infant botulism? He is off balance and constipated.

Rare but possible. Infant botulism is rare; most cases occur in babies under 6 months old, but it's possible in a 10 mo.old. Constipation is often the first symptom but I wouldn't be too concerned unless he develops other symptoms such as muscle weakness.Symptoms develop 3-30 days after eating.See
https://kidshealth.org/en/parents/botulism.html
and https://www.poison.org/articles/2010-jun/dont-feed-honey-to-infants.