Thank you for your question!
There are no products, vitamins or supplements that have been shown to be effective or beneficial for the immune system in adults and children.
Instead, look at non-pharmacological measures: make sure your child eats plenty of fruits and vegetables, gets adequate sleep, and manages stress well if possible, among others. If one of the children or members of the household is sick, simply maintain basic hygiene measures: avoid hugging if possible, do not share towels, and wash them often.
Finally, if your child is prone to colds, I strongly suggest, for maintenance and prevention, sinus hygiene with a saline solution like Hydrasense or Sinus Rinse.
This is the best option to prevent the accumulation of secretions. There is no maximum during the day, but it should be done at least 30 minutes before bedtime.
I hope I've been helpful, and I'm available if there's anything I can do
Tom Samaha, pharmacist