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The cluster of findings you describe are certainly consistent with viral conjunctivitis, in terms of eye findings and swollen lymph nodes in the neck. However, the spots/rash on the skin do raise concern about the overall diagnosis. On the one hand, this could be a self-limiting viral flu-like condition. On the other, there are odd infections that can cause rash, flu-like symptoms, headache and conjunctivitis. (May require oral aantibiotics.)
As far as the eyes are concerned, it would be worth showing them to an ophthalmologist if there is any redness of the white of the eyes, or if the vision has deteriorated. I think that in any case it would be worth getting checked out my your family physician, especially if there is a temperature.
I hope it all resolves soon. If the advice is helpful, kindly click the 'accept' link.