I know that with my kids the doctor said that if it is just one eye it won't be an allergy...And allergy would affect both eyes.
(Although I wouldn't completely rule it out ---say if he touched something he was allergic too and then rubbed an eye - well it might affect just that eye)
If no one else has had a similar symptom it probably isn't pink eye either---pink eye is highly contagious.
The other possibility is that he might have a blocked or partially blocked tear duct. BUt I think you would notice fluid building up.
You might call one of of the ask a nurse lines over the weekend. THey can run through a bunch of questions to narrow down what it might be. And they can sometimes help get into the doctor faster - depending on if you doc is part of that practice.
If it were my kiddo I would likely take him to urgent care- our doc has an office open on Sat. and Sun that charges the regular co-pay......(I had one kiddo who had a blocked tear duct and pretty regularly had pink eye her entire first year of life-- she had her first infection before we left the hospital!)