Eye Problem

About two weeks I adopted a young parakeet from an old lady living near me, but the bird has a little problem with his eye that gets worst on stress.

Take a look on the picture bellow (not the best shot since I'm restricted to my cellphone camera now).

this reddish area bellow his eye is a little swollen all the time. This red area doesn't seem infected at all, don't have pus, and don't look like other conjuntivitis I've seen...

but it gets a lot worst when he gets nervous or irritated (for example if I chase him or grab him), it get a lot more swollen, once to the point that he got his eye closed. After some rest it gets to it "normal" state, a little swollen that doesn't seem to incomodate the bird.

I started last night to clean the area with a boiled water and sodium solution, it looks like the swollen is better, but still I'm not sure if what I'm doing is the best for him, I'm currently living him alone to rest and only grab him to clean the afected area.