Sir I got a problem as my toe's nail inserted to the side of my mass and it causing severe pain and also a smelly pus. I went to a doctor and he cuts the half part of my nail but the mass or flesh is not healing and on the other side the nail is growing

See a qualified DPM. Proud Flesh on the corners are related to the ingrown nail. Not unlike a splinter. The odor is an infection usual superficial. See a podiatrist and have the nail edges removed and the matrix destroyed. The procedure is called a P and A nail procedure.
Fix it Right. It sounds like you are suffering from a severely infected toenail. The mass or flesh you describe growing on the side of the nail is granulation tissue. It is not clear as to whether this infection involves both sides of the nail. Removing part of the nail is only part of the treatment. All the granulation tissue must be remove. , whether one side or both. Antibiotics and daily soaking are a must.