Thank you for writing to us.
Most likely the "one-sided headache" that you are having is as a result of blockage of your nose resulting in blockage of your sinuses
and leading to the type of headache that you are having.
Sinuses are air filled spaces that are present in the skull and all of them drain into the back of the nose (not visible to us).
When one has a cold
the nose gets congested and the sinuses have the tendency to get blocked.
There is a sinus in the head that is called as the frontal sinus.
When the sinuses get blocked they can cause one to have headache on the side of the head where the sinus is blocked.
I would strongly recommend that you should contact an ENT doctor for further evaluation of your condition and possibly do further tests like an x-ray of the sinuses or a CAT scan of the sinuses to be sure.
I would also like that the ENT doctor should examine your nose to see if you do, or do not, have a deviated nasal septum
which can also cause such kind of a problem.