The short edge is your constraint: 2300 pixels for 20 inches is 115 pixels per printed inch. So, you don't have a ton of scaling up to do. Depending on the print medium and the subject matter, 150DPI is probably enough, and maybe 115 DPI is already enough - especially if you're printing on a textured surface like canvas. Photoshop should get you there just fine, or OnOne Perfect Resize (formerly known as Genuine Fractals in previous versions) will do too.
I personally just had a bunch (sixteen) of portrait prints done on glossy vinyl mounted to foamcore, at 18x24. The print service recommended 150DPI, and I was skeptical but that's what I sent them - and they turned out great. Even inspecting up-close with a photographer's scrutinous eye, there was no pixelation or graininess or blurriness.
Perhaps just as important at the issue of scaling up: you're going to have to crop the length down from the approximate 3:2 ratio of your current image. 20x24 is almost square, by comparison.