First of all oxygen enters our body by inspiration (breathing in) through our mouth and nose and gets transferred into the lungs. During this process the diaphragm lowers below the lungs and the rib cage expands. This is what gives room for air to enter the lungs. Under normal breathing air enters in to the lungs automatically without much effort. This is called the tidal volume which is relatively small, considering that our body can forcibly inhale six times that amount with effort. The oxygen in the lungs gets transported to our bloodstream passively which means that there’s truly no way for a person to naturally modify the way oxygen gets into our blood.
However, when a person holds their breath the uptake of oxygen into the bloodstream gets disrupted. The temporary holding of breath by exertion is called the Valsalva maneuver.
Several bad things can happen when you hold your breath.

Deficiency of oxygen in the muscle tissue resulting in more rapid muscle fatigue

The force of holding one’s breath increases chest pressure

Increased chest pressure compresses the heart resulting in an increased force of blood flow and rapid increase of blood pressure with greater stress on the body

The end result can be dizziness, lightheadedness, and even loss of consciousness.

These are the last things you need to happen when recovering from an injury. The muscles, bones, joints, and all of the connective tissues that are involved in various injuries are already at a disadvantage during the healing process. Adding extra stresses by being deprived of adequate oxygen can be detrimental in returning to functional mobility and strength levels.