Dropsy is just an old word for edema, a condition where there is an accumulation of fluid in the body causing swelling.
If left untreated, edema can cause:
Increasingly painful swelling
Difficulty walking
Stiffness
Stretched skin, which can become itchy and uncomfortable
Increased risk of infection in the swollen area
Scarring between layers of tissue
Decreased blood circulation
Decreased elasticity of arteries, veins, joints and muscles
Increased risk of skin ulcers
(Mayo Clinic)