I had some acrylic sheets from old Melissa and Doug toy boxes, and needed some arm protectors for archery for myself and the kids (I later used more of the acrylic for a bow sight
). A bit of work with hair dryer, box cutters and rotary tool, and I made some that work fairly well, though they are somewhat difficult to put on over clothes (Velcro might work better).
The arm protectors have two functions: one is to protect the arm from string slaps, and the other is to keep clothes out of the way of the string. The smooth plastic also may mean that if the string goes on the protector, it won't distort the shot extremely (though it will distort it significantly).
These are usually made of leather, but I don't have any scrap leather.