Vit C and zinc are at best preventatives and do nothing to reduce the duration of a URI (cold).
Fluids are important just to keep your secretions more liquid.
Paracetamol (acetomenophen) sounds like a help for your head or fever if (when ) you experience it but you may well need a decongestant to open your sinuses (why your head hurts in the first place) Pseudoephedrine or Phenylephrine (if you have no hypertension concerns).
No one has mentioned getting a vaporizer but it helps keep the humidity in your room up and reduces the rawness to your throat. If you start having a cough, guafenisin helps thin out the secretions and dextromethorophan can decrease the dry cough.
All these are OTC and just look at the med labels to find them. Avoid those with paracetamol in them as you will get a double dose which may poison you.

It is important to treat colds as the duration without treatment can be as long as 2 weeks but the duration with treatment is only 14 days.

Drink scotch