I wake up at night worrying. Will this harm me?

Kind of. It leads to sleep deprivation unless you're able to get back to sleep long enough. This is a symptom of anxiety disorder and you should seek help for this with your doctor.
Woken worry. The only harm i see is disrupted sleep and inadequate rest. In time this can be problematic as you may fall asleep , while you drive, have irritability in day time, disrupt your productivity and relationships. Sometimes worries are the manifestations of fears either real, exhagerated, unreal, all of which sometimes may be best to unload or discuss with a trusted friend, family or professional.