I've got some bad news for you. It's probably your monitor. CRT's get old and start to have problems like this. You can try bumping up the refresh rate and see if that helps; it sometimes does for a little while, but I wouldn't count on it.
The fact that the red tint doesn't show on your TV is a pretty good indicator of this. If the monitor is really dear to you, then you could try to get it fixed, but it usually isn't worth it as it's very expensive to repair CRT's.
I suggest you start looking for a new monitor. If your interested in LCD's, there are some great options out there: check out BenQ and Viewsonic; those are often considered some of the 'best' brands. Take a trip to BestBuy and check out some monitors to see what you really like.
CRT's are still available if you want to go that route too. I think Newegg and Tigerdirect still carry some.
Oh, and isn't it fun trying to take a picture of red with a red-eye reduction feature on your camera?