When your print shop is checking the resolution of your file, they assume that you want smooth looking ordinary photos with no visible pixels. Your case is special. You actually want the pixels to be very big and visible, so in your case the low resolution is not an error.
The worst thing that could happen to your artwork is if the print shop upscales your image using something like bicubic interpolation. This is a method to enlarge images while avoiding visible pixelation. In your case it would result in blurry edges.
There are several ways of avoiding this problem (although most of them requires some knowledge and/or graphic application):
You could make sure that your png-file is actually a true 1-bit (B/W) image, and not just a color or grayscale image resembling a binary image. Then it should rescale with jagged edges (which is what you want). But, you can't be sure that the print shop doesn't convert your image when you upload it turning it into a grayscale or color image. That is a risk.
You could manually upscale your 1-bit image to a larger resolution. It should be 1200 pixels/inch, so the dimensions of the upscaled images should be
18" * 1200 ppi x 24" * 1200 ppi = 21600 x 28800 pixels (BTW: Your posted image is actually not 2000 x 2664 px as stated but 2000 x 2500 pixels - which makes more sense). There is still the risk though that the print shop will convert your image to grayscale or color resulting in slightly blurry edges.
You could make a pdf-file on the correct dimensions (18" x 24") with the 1-bit images (must be true 1-bit!) placed inside. Sketch should be able to output this.
You could make a pdf-file on the correct dimensions (18" x 24") where you have made a manually or automatically vector trace of your images.
I would go for solution 3 or 4. I would never upload an image (png/jpg/tif) to a printing service because I am unaware of what they do to the image. I would always use the PDF format since it "knows" its own size and can contain both pixel and vector graphics.
I know this answer might be "a bit much", but I can't really simplify it anymore. Feel free to ask additional questions.