The best thing for that you just go to a drug store or grocery store- pick up some "Bag Balm". Otherwise, there are some other products that are good for it, like Neosporin or 3M skin scare, but the bag balm works very well. For now, try taping or bandaiding the cuts so they dont get worse while playing. Lotion during the day can help too.
Solinco Tour Bite string