If I think I have a rotator cuff tear should I keep my arm in a sling until I can go to the doctor?

Part of the time. If the shoulder is very painful you could use the sling for comfort, but you should remove the sling frequently. It is important to avoid strenuous activity, heavy lifting, pushing or pulling until you are evaluated. However, a condition called adhesive capsulitis, or "frozen shoulder", can develop quickly if the joint is completely immobilized for too long. Do light, assisted movements.
Not necessarily. If you have sustained an accident and are in severe pain which is worsened by range of motion, a sling can be a good temporary means of pain relief and is fine to use until you seek medical evaluation. If you are having pain and weakness raising the arm (common symptoms of rotator cuff tears), you should see an orthopedic sports or shoulder specialist but don't necessarily need to wear a sling.
Slinging is not... Necessary but if you are more comfortable in a sling, i would not hesitate to use it. Thanks and good luck.