When a boyfriend breaks up and then constantly phones the person he broke up with he may know he has made a mistake and it is up to you to ask if he wants to get back together again if that is what you want. People are just human and can make mistakes. Your boyfriend could have possibly been afraid of commitment; he could have had a stressful day or he is not independent and may feel he was going to lose you. Get together and talk to each other and sort this problem out so it ends one way or the other.
No, it is not a bad thing if your boyfriend breaks up with you after one week. Young men have raging hormones and they can flip from one girl to the next. Don't feel bad. It would be wise of you to start dating again and he may come back if he sees you are not moping around for him, but, if he doesn't then you weren't meant to be together and there is someone special out there for you.