Minor side effects. Some lesser side effects experienced with insulin glargine likely will not need medical attention. Minor side effects will disappear as your body adapts to the medicine while receiving treatment. Furthermore, your doctor might be able to advise you of ways to prevent or decrease some of these side effects. However, should any of the side effects listed here continue, are disturbing or you have questions concerning them, talk with your doctor. The minor side effects include thickened skin at the point of injection, fever, redness or discomfort at the injection site such as swelling or itching, sore throat, depressed skin at the point of injection, and runny or stuffy nose.