The swollen skin (in the right side of the toenail) is called hypergranulation tissue, usually from pressure from an ingrown toenail pressing into the flesh.
Some people feel no pain or discomfort, whilst others complain of extreme sensation. This may actually be a lingering sensation from the stubbing or the ingrown pressure.
Granulation tissue is comprised of new connective tissue and tiny blood vessels, that form on the surfaces of a wound, during the healing process.
The wound from ingrown toenails will not heal when there is hypergranulation tissue. This is because it will be difficult for epithelial tissue to migrate across the surface of the wound, and contraction will be halted at the edge of the swelling.
Hypergranulation tissue should be excised if present.