Dog Is Lethargic, Nose Is Dry, Cries If I Touch Under Chin But I Don't See Any Sores, What Could It Be?

Lethargy is a condition due to some underlying causes. It is characterized by having

1. Reduced activities
   
2. Drowsiness
   
3. Delay in response to external stimuli

Persistent lethargic signs in dogs can be due to some serious illness like

1. Electrolyte imbalance
   
2. Anemia
   
3. Cardiovascular disorders
   
4. Infections
   
5. Hormonal disorders
   
6. Cancer
7. Skin and eye diseases
   
8. Toxic reactions
   
9. Side effects of medicines
   
10. Immune diseases
    

Dry nose does not mean any illness and wet nose does not mean that a dog is healthy. In my opinion, you should visit a vet.