Final answer:
The described skin inflammation could be eczema, but it closely matches the characteristics of impetigo, a skin condition causing lesions, small blisters, and encrusted sores often around the nose and mouth.
Step-by-step explanation:
The skin inflammation characterized by dry or moist lesions, an eruption of small vesicles and a water discharge is called eczema. However, the description also closely aligns with impetigo, which is known for causing dry or moist lesions, as well as vesicles, pustules, and sometimes bullae that often form around the nose and mouth. The nonbullous form of impetigo leads to vesicles and pustules that rupture and become encrusted sores with a typical yellowish crust and exudate.
In contrast, bullous impetigo involves larger fluid-filled blisters that rupture, resulting in larger, draining, encrusted lesions.