Are you sure you are not getting the credit? It should be on Form 1040 line 19.
Is your son listed as a dependent on page 1 of Form 1040? If not, that's why you're not getting the credit.
The credit for other dependents is nonrefundable. That means it cannot reduce your tax below zero. If Form 1040 line 18 is zero your tax is already zero, so you cannot get the credit for other dependents (or any other nonrefundable credit).
The credit for other dependents is phased out for high incomes. If your Adjusted Gross Income (AGI) is over $239,000 ($439,000 if married filing jointly) the credit for other dependents is completely phased out.
(The phaseout is actually based on Modified Adjusted Gross Income (MAGI). For the credit for other dependents, MAGI is the same as AGI unless your tax return includes Form 2555 or Form 4563 or you excluded income from Puerto Rico.)
