It looks like you have developed sinusitis as it can cause these symptoms. You may need to do an anti-biotic course. I would advise you to see an ENT specialist to confirm the diagnosis and start treatment. Thanks.
Cough would be due to the sore throat that you had. Some infection still seems to be present. It has lead to infection of the sinus which is causing you these headaches. An anti-biotic course of something like Augmentin should help after doing the culture tests. Thanks.
Although, you are just 29 years of age but if your problem persists I would advise you to get an MRI of the spine done to rule out cervical spondylosis. I thought you were having headache on moving your head because of sinusitis. But now it looks like cervical spondylosis. Even meningitis can cause neck stiffness but it would have fever and other signs. You should see a doctor as examination is important. Thanks.