Yes, novocaine can make your lip swell. This is because novocaine is a local anesthetic that works by numbing the area where it is injected. When injected into the lips, the novacaine can cause the blood vessels in the area to dilate, which leads to swelling. In some cases, people may also have an allergic reaction to novacaine, which can further contribute to swelling. If you experience any swelling after receiving a novacaine injection, it should resolve within a few hours.