No. Full time student only extends the age for a Qualifying Child from 18 to 23. There's nothing additional, until you start paying college tuition. 

Your problem is that your "qualifying child'' turned 17 and no longer qualifies for the child tax credit. This comes as a big surprise to many parents the year their child turns 17. A child over age 16 no longer qualifies for the Child Tax credit (CTC). Although a child can still be a student dependent through age 23, and a qualifying child for EIC,  the Child Tax Credit expires the year they turn 17 and you no longer get the $1000 CTC.