The T-Shirt Screen Printing field is an option for any Graphic Designer, and you do not necessarily need any degree at all. Proficiency in Corel Draw and to a lesser extent Photoshop are both important. Also an understanding of how the Screen Printing process works is very useful, as making a design look good when Printing on T-Shirts and other apparel isn't always the same as making it look good on a computer monitor.
There are Screen Printing companies everywhere, from small 1 or 2 person shops to large Printing Warehouses with quite a few artists. I'm not sure if this is appealing to you or not but knowing how many people are in the Graphic Design field and how competitive it can be, as well as the number of independent Screen Printing shops, I think Graphic Designers in general would be well advised to explore this area. As I said, to be a successful Screen Printing Graphic Design Artist you must have some understanding of the Screen Printing process so that the artwork you create will print easily and well. Here's an article that describes some of the Screen Printing Process:
Here's a forum for some general info:
Oh yeah, one more thing, Screen Printers in general are not very "corporate" and don't care about degrees, it'll be your abilities, knowledge, and portfolio that make the difference.