The CC MUST inform you even if it is a small cut. It is their responsibility. Bite marks is pretty normal in toddler class but still it should not happen too often. You should be able to reach the firm teacher on a daily basis. There is no excuse that they will not attend to you when your child is in the centre. Is there a communication book or portal where you can write to the teacher daily? For some school it is a requirement that the teachers update the communication books daily. For certain schools they have e-portal where you can communicate with the teachers. The teachers should not be invisible. You are not expecting too much. I was working in the CC before. Such requests are a norm.
Hope this will help.