General rule of thumb is to start weaning kitten by the time they reach 4 weeks of age (source: pets.webmd.com). I guess the mother being injuried and her crying is due to the fact that your kittens have already started growing their baby teeth - a thing that kittens usually do as early as at 2 weeks of age. Not only their chomps are now more damaging, but also the teething process itself creates a discomfort which could cause excessive chewing, resulting in them abusing the mother's nipples and causing bleeding injuries.
But the weaning process should optimally be significantly stretched in time and not finished until about 6 to 7 weeks of age. Although it should optimally be started at 4 weeks of age, at 3 weeks of age you already could slowly and carefully try introducing soft, wet food to provide a little relief for the mother cat - but please note that this absolutely needs to be a slow and gradual change.
What is more, please make sure you're feeding mother cat a nutrition-rich, high quality food. For instance, she absolutely needs to meet her recommended daily intake of protein to physically have the building material (amino acids) for regenerating the damaged tissue of the nipples. Also, for example, zinc is required for proper wound healing because it plays a major role in all phases of this process. If you are feeding the mother cat with a specialized and high quality food explicitly made for nursing mothers, all these essential nutritients would be there in adequate amounts.
It is also important now to frequently clean these bleeding wounds so they could properly heal. I'd suggest flushing them a few times a day with sterile, isotonic (0.9% NaCl) saline solution from your local pharmacy. Please avoid using hydrogen peroxide and alcohol-based disinfectants, as they are too caustic and could cause negative interference in both the wounds' healing process and the nursing of your kittens.
I'm also a little worried about the possibility of the mammary gland inflammation (mastitis) of the mother cat. It could happen if these wounds were to get infected and pathogens were to enter the mammary gland through the teat canal. At the same time, weaning the kittens too soon could theoretically also cause an infectionless mastitis due to prolonged milk accumulation without removal. But it is hard to tell over the Internet.