I am a Reg. Nurse. I had a similiar experience about 3 years ago. The cut was really bad but it did heal and did not get infected. It took almost 4 weeks to close up completely. Keep an eye on it and if you think it is getting infected, see a doctor right away. I kept mine bandaged most of the first 3 weeks. It also taught me to be much more careful when cutting. Hope you will be OK.