Pain down the sides of the toenails is reasonably common and almost always gets called “ingrown” when most cases are not actually ingrown toenails. A true “ingrown nail” is when the nail has actually grown into the skin, penetrates the skin and can become quite painful and is usually infected.
Most cases of pain down the side of the toenail are not due to an ingrown nail actually penetrating the skin but results from pressure from the curved nail down the side in the nail grove. While that is not technically an ingrown nail, it is trying to “ingrow”. What happens is that the skin responds to that pressure in the nail grove and become thicker causing a callus to develop in the nail grove. This callus then becomes thicker in response to the pressure and it is that thickness of the callus in the nail grove that causes the side of the toenail to hurt in the absence of a true ingrown toenail. This is technically called an onychophosis and is not an ingrown toenail.
To get pain relief for the side of toenail pain from an onychophosis, a skilled podiatrist can carefully debride it and file the edge of the nail away from the painful area.