Is there a non-surgical remedy for gynecomastia that I can do myself?

Possibly. Some gynecomastia is related principally to fat deposition in the breasts associated with being overweight. Getting back to ideal body weight in this case will reduce breast bulk.
No. There is not a home remedy for true gynecomastia. If the breasts have enlarged due to an increase in body weight and fat, then weight loss is the answer and it is controllable at home and self directed.
Treatment available. For men with gynecomastia, a doctor can evaluate and look for disorders that increase the amount of estrogen-type hormones in men, such as liver disease, alcohol use, marijuana use, obesity, etc... Sometimes gynecomastia happens without an obvious reason. Non-surgical treatments such as estrogen blockers (tamoxifen is one) have been tried with some success. An endocrinologist doctor may help.