As mentioned, simplified damage would make sense.
For example:
If you get shot in the leg by a 9mm, then you should not be able to sprint for a while. After a little while though, you can sprint, but it will drain stamina quicker.
A shot from 7.62x54R in the leg would disable running until you respawn.
Whenever a play is injured, they should loose stamina quicker and will experience more weapon sway. But it should be dynamic. For example, being shot in the arm will create more weapon sway than being shot in the the leg. But, being shot in the leg will decrease stamina when running more than if the player was shot in the arm.
Adding bleeding, bandaging ect. would make it a little too complicated and would not be good for gameplay IMO.