festering (often figurative), oozing, open, running (esp. BrE,often figurative)
This issue is a festering sore between the two countries.
The border dispute was a running sore in relations between the countries.

cold
I have a recurrent cold sore on my lip.

canker (AmE)
canker sores caused by biting the inside of your mouth

bed (usually bedsore), pressure, saddle
Many people in the care home have bedsores.
I get saddles sores on the right side.

cause
develop, get
The patient developed pressure sores on the toes of both feet.

have

Sore is used with these nouns:
arm, back, elbow, hip, joint, knee, limb, loser, mouth, muscle, neck, nipple, point, shoulder, spot, throat, wrist