You didn't state if the pus comes out from the nail bed
, but if it is, its probably a cuticle infection
you have got.
You need to use hydrogen peroxide, which decimates the germs. You could use alcohol, even though it burns.
You could make a dressing, so that there is less exposure to water, and germs.
Make sure you change the dressings at least twice a day, and allow some air to blow on it for some time.
Then, you could use cuticle creams subsequently to massage your cuticle.