I don’t know if “20 minutes” is always a realistic limit.
While slicing a vegetable with a newly purchased, very sharp knife, I cut off a chunk of a finger tip. I was tempted to go to the emergency room. Instead, I wrapped the injured area with gauze and adhesive tape. It took about 24 hours for the bleeding to stop completely, and a week or so for the skin to grow back.
I also included a specific request for healing in the relevant blessing of each Shemoneh Esrei,
But that’s just my personal experience.