My doctor just prescribed me nortriptyline for an anti-depressant. Is this common?

Somewhat. We don't use notripytline as much as we used to, but it is still a good drug. Selective serotonin reuptake inhibitors (ssris) are the most prescribed nowadays because of their safety profile. Nortriptyline can be good for depression and anxiety as well as sleep, pain, wetting the bed, and headaches. Take it exactly as prescribed, though. Too much can be bad for your heart.
No, but a good med. Nortriptyline is an older tricyclic antidepressant. It works mainly on norepinepherine rather than serotonin like the newer drugs. It is just as effective as the newer medications, and for some types of depression may actually be more effective. It has some additional side effects that your physician should check for.