The invention relates to the novel cotton variety designated 16R338B3XF. Provided by the invention are the seeds, plants, plant parts and derivatives of the cotton variety 16R338B3XF. Also provided by the invention are methods of using cotton variety 16R338B3XF and products derived therefrom. Still further provided by the invention are methods for producing cotton plants by crossing the cotton variety 16R338B3XF with itself or another cotton variety and plants and seeds produced by such methods.