I experiences the same ... giddiness, however "headache" are symptons aka migraine...throwing up frequently regardless of day or night.. there's even one mid-nite that I totally couldn't take it and i urge my hubby to come back home as he is working night shift,to bring me to hospital.
The hospital doctor couldn't prescribe "strong" medicine due to pregancy. Anyway, the medicine that at last he prescribed is working - I felt asleep almost immediately after taking it,partly maybe due to exhaustion.
If you do not have any "throw" up or migraine like symptons, it is probably "morning sickness", however, if you do feel nausea take some ginger tea may help and also soothes the headache/giddiness.
And if is bad and be aware of dehydration that might affect the baby then better see your gynae - he'll be able to help.
Hope it helps : )