Is it possible to manually design new patterns on tee shirts so my characters willl convey any message appropriate to my story?.

drawn

The shirt's mesh should have a UV template associated with it which is normally found within the object file.  If such a template does not separately exist, you might need to rely on a third-party app to unwrap the object file and save the template as a .jpg file.  The .jpg image will need to be opened in another third-party graphics program so you may place and center the design of your choice.  It is best that you have a high-resolution image or text for it to be legible in the final render.

Another simpler alternative is to locate the texture file for the shirt and open it in a third-party graphic program.  Create the design in a separate layer and position it exactly where you want it.  Merge the layers and save the image as a .jpg or .png file under a different name.  In Poser, replace the original texture file with the one you created.

My son goes to redbubble to get his designs printed on t-shirts etc.

You're kidding?

You're kidding?