How to print enlarge my computer painting

If you used a program like Photoshop that creates raster images then you're going to lose resolution when printing something larger than the canvas size you used in the app: moreso if you kept the "dots per inch" setting at 72 with is the default).

Corel Painter seems to be a raster-based app as well so it may have the same constraints. Not fully sure.

Either way, you'd want to look for a commercial-printing place.

Have you tried using GIMP to resize?

It needs to be made using a vector-drawing software to be able to be resized. Otherwise there will be quality loss. Also VectorMagic is a software than can convert a normal image to a Vector. Not as well as a human, but quite a decent job, allowing it to be resized to whatever dimensions are needed.

Normally printing needs a minimum of 300dpi. For best results you'd need to convert the image to CMYK with print-safe colors, as not all colors shown can be printed accurately. Also ink tends to bleed, and so that is another thing to keep in mind, when working with images containing text.