I don't know if it's intended or a bug. But I just recently learned the first word for drain vitality & when I cast it. It has no words spoken like my other shouts. If this is a bug is there any way to fix it?

Yes, this is the infamous Marked for death/Drain Vitality bug. If you install the Unofficial Dawnguard patch it will be fixed immediately. I also recommend the unofficial patches forthe other DLC's and Skyrim.