Red eyes

Could someone tell me what's up with my eye ?

This happens to me a lot in the winter.

I look at screens a lot and face a florescent light in a low ceiling at work for 8 hours straight every day with a half hour or so break. One is 20" and the others 24".

Could that have something to do with it ?

They're itchy, and sometimes it feels like one'll start bleeding or something.. It always starts in the same place on the left eye, and if that gets worse the other one goes red.

Sorry if not the best place to ask. :s