I'm headed to bed but here a few ideas to get your name and painting across through a logo

-Make a T with that looks to be 2 brush strokes, then add a second smaller cross in the top/middle representing 2 T's and Painting, throw it in a circle, whether tit be solid or a brush stroke outline, simple.
-Brush stroke your name
-Make it your signature that you sign on your paintings
-Endless possibilities with symmetry using 'T T'

looks very design-y

i would say make it as minimal as possible and let your work speak for itself.

1st, why the hell would you say you got bad initials? 2x the same is always easy to play around with
2nd, maybe your font comes out pixelish because you made it in photoshop and used sharp edges on the font? (at my photoshop this is the auto selection)...it's also possible that you or the site you uploaded it with made the image a low res one

suggestion: mby try play some with caligraphy, as illustrator i'm sure you can manage to make something sweet out of that?

IDEAS