Just like they can be allergic to bug bites or to some food ingredients, dogs can also develop an allergic reaction to sheets. Of course, you probably won't be able to determine exactly which allergy it is, therefore, if you notice scratching, itching, and coughing in your dog, you should consult a veterinarian. Also, you should take care that your dog’s surroundings are always clean. All things inside your dog's bed - bedding, blanket, pillow, toys - should be washed and maintained regularly.