How do I fix my crt television problems?

I don’t think the problem is with your TV. I think it’s with your cable box.
Most CRT televisions in my experience aren’t digital. If this isn’t a digital TV, then the artifacts you are seeing are coming from upstream of it, since I’m pretty sure they are digital artifacts.
Just to be sure, do you have another TV to test with the converter? If the problem persists with another TV that is known not to have the problem when working with a converter box, then you can eliminate your TV as the source of the problem.

I agree. There’s nothing about a CRT that can pixelate an image.

@dabbler and @rex have it correct. An old CRT TV is analog – not digital. It doesn’t pixilate – it simply can’t.

Pixillation is generally a symptom of a damaged (or dirty = incomplete) digital signal coming from the source to the digital decoder. In other words, the digital cable signal coming into your cable box is crap.

@dabbler @elbanditoroso and @rexacoracofalipitorius are mostly correct, mostly.
The problem is either your decoder box or the signal you are getting, which could include the original source from the TV station, but probably isn’t.

Have you tried at least to unplug the cable-company wire from the cable-box, and plug it back in?

That is probably actually a twist-off/on co-ax cable. To take that off you’d unscrew the big nut at the end from the connector on the box, then pull the cable out.
To clean the connection of oxides work the center wire into the connector and back out a couple times.
Then center the middle wire into the connector, snug it up then screw it back on.
If that is a short cable to the incoming wire do the same thing at the other end of that cable.

Maybe you did that already…