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The symptoms mentioned by you can most probably be due to viral infection or a gram positive bacterial infection( like pharyngoconjunctival fever
The treatment for viral infections is mostly supportive while a bacterial infection needs a course of antibiotics .
The confirmation of diagnosis requires a thorough evaluation and investigation by a pediatrician
and treatment can be started accordingly with antipyretics analgesics and antibiotics .
The eye drops seem appropriate and the red spot can be due to an engorged or inflamed blood vessel.
As of now you should try the following .
1. Give the child plenty of fluids ( water ,soups etc)
2. Rest for the eyes , frequent cleaning with water and eye drops as prescribed , avoid scratching , rubbing.
3. The fever can be controlled with prescription drugs like acetaminophen
4. The cough is mostly due to congestion and irritation and might be better with saline gargles , steam inhalations thrice daily and decongestant cough syrups with chlorpheniramine
Hope this answer is helpful for you.
Wishing your child a speedy recovery.