is this something that developed overnight or did you notice a red tint in the picture all along?
I would say if you know what I'm talking about, swap the red transistor on the neckboard with the green or blue ones and see if you get an all green or all blue screen. if that happens, then the transistor is bad, your tube is fine, and that's the easy solution.
if it winds up being the tube, then you might have a fix that lasts you a long time if you rejuvenate it, and you might have one that lasts you a few weeks and it goes back to doing what it was doing.
if you have no idea how to go about either approach, my best advice for you is to NOT take it to a TV shop and to go headhunting for people that live nearby you that work on monitors and preferably own a rejuvenator.