There is a slight chance you may be in luck. If you, like most people are a bit off on the age of their electronics, it might be a PTK195 based set.
Those sets had a known issue with the PS for the convergence and have put out an updated PS.
Now usually forget about TV repair unless your a pro. I don't care if you do MRO or even installation of robotics, or work on aircraft, this is a different animal. My uncle was a tech specialist at IBM and I was the TV man. Of course he would take a crack at it, but in later days I would get the call. Ironic, he fixed our first color TV back in the tube days and it wasn't a tube ! You need specific knowledge for this newer stuff.
So forget component level, for that you need a pro, but there are two quick things you might be able to do. If it is a PTK195 you can most likely install the updated power supply board. If you can solder and know safety (like discharging caps) you can update the PS chip from an STK730-??? to an STK730-180 (IIRC). I found that simply replacing the chip with an equivalent fails most of the time. The 180s seem to hold up.
When it's something like this a little DIY can help. I don't want your set sitting in the shop waiting to get scratched or something waiting for parts.
If you're not a tech I suggest you call a shop, but you can save a few bucks if this is a 195 based set, you can pull the box, which includes all the CRTs and everything. A competent shop can tell if the problem is fixed, and will most likely insist on reinstalling it themselves so they can check convergence and geometry, as well as magnetic centering, which if off too far can cause the exact problem you have. Also, if you pull the box yourself, remember to disconnect the cables to the speakers and keyboard, otherwise you might wreck them. You do not need to remove the keyboard or speakers, that is unless you rip the wires out of them when you slide the box out, then you might have to replace them.
It's not hard to see how to do it once the back is off. I'd call around first if you go this route, and get another person. You can carry the box alone but you can't get through doorways etc., the handles are on the sides and it is too wide.
Last but not least, save that set if the picture is still good, and when it finally dies DO NOT buy another RCA ! They changed everything and are no longer sevicable this way.
JURB