Is it permissible to benefit from the Institute's Zakat fund to cover the medical expenses of my son, knowing that I have money invested in trade that cannot be withdrawn until the end of the year?

The scholars have determined that the expenses for a child's upkeep and education are to be covered from his own wealth if he possesses any. If he does not have wealth, then the responsibility falls upon his capable father. In this situation, the father is not permitted to accept Zakat (definition) for the child's education, and if he does take it, he must return it. Since you are wealthy, your child is considered wealthy through your provision, and his education costs are part of these expenses. Therefore, you must sell a portion of your business or borrow money to cover his education costs.