Bringing me to my point; I have athletes, very commonly, be too stubborn to use crutches when they sustain minor lower limb injuries.
True enough, the pain isn't so severe that walking isn't impossible, albeit with a limp (as was the case for me.) But, despite the fact that you might feel "soft" for using the assistance, the fact of the matter is that you're prolonging your recovery time by limping around.
When an acute injury occurs, we know that consistent movement and range of motion are crucial in those early stages in order to promote proper tissue healing. In the event of soft tissue damage, scarring will start to form. Taking the joint through its regular range of motion means that that scar tissue, as it forms, will align itself in those directions of pull, developing as closely-resembling the healthy tissue as possible.
When limping and protecting that joint, you're preventing proper movement and avoiding stressing that healing tissue, resulting in irregularities in the scar formation. This is likely to prolong the pain and potentially result in mechanical dysfunction later on in time. Conversely, using that walking assistance allows you to deload the limb while maintaining regular (or as close to) movement of that joint and increases the speed and effectiveness of healing.
So, I know that you may not expressly feel the need to use a cane or a crutch when in minor pain from an ankle sprain, hamstring tear, or other lower limb injury. However, buck up and use the assistance until you can walk without a limp; you'll recover faster and stronger for it.