As Margot said, it may be a cyst or abscess
. I don't know where you
live, or what diseases are present in your area, but if it is a cyst or abscess, then it isn't contagious. But do be careful to wash your hands with hot water and soap after handling it ir bathing the wound, etc, as sometimes infections like this can cause stomach upsets, if the bacteria are transferred to your mouth or food etc.
At one month, he is really young and tough in his little way...yet also very vulnerable.