I’m 5’4" and weigh 250 lbs. Should I have the gastric sleeve? (Photo)

Congratulations on considering this important step to improve your health!
With a BMI of 43, have obesity (defined as a BMI >30). Obesity puts you at risk for obesity-related co-morbidities such as type II diabetes (T2DM), hypertension, sleep apnea and other respiratory disorders, non-alcoholic fatty liver disease, osteoarthritis, lipid abnormalities, gastrointestinal disorders, and heart disease. Thus you are wise to be concerned about your weight, its impact on your health, and the increased difficulty to lose weight or undergo surgery as you grow older.
To qualify for gastric bypass surgery (aka weight loss surgery), the American Society for Metabolic and Bariatric Surgery recommends you meet one of the following:
BMI ≥ 40, or more than 100 pounds overweight.BMI ≥35 and at least one or more obesity-related co-morbidities such as type II diabetes (T2DM), hypertension, sleep apnea and other respiratory disorders, non-alcoholic fatty liver disease, osteoarthritis, lipid abnormalities, gastrointestinal disorders, or heart disease.Inability to achieve a healthy weight loss sustained for a period of time with prior weight loss efforts.
From the information you shared, you meet the first and third qualifications. Meeting with a bariatric surgeon in your area will allow you to further discuss the pros and cons of surgery as well as insurance coverage and the cost for the surgery in your geographic area. You can also check out the Patient Learning Center of the American Society of Metabolic and Bariatric Surgery to educate yourself on surgical options.

Deciding to have the gastric sleeve is a personal choice, but based on your weight and BMI, you could be a good candidate. Since your BMI is over 40 and previous attempts with diet, exercise, and medication haven’t worked, bariatric surgery may be an effective long-term solution. The sleeve can help you lose a significant amount of weight, often around 60-70% of your excess weight, which could get you close to your goal of 170-180 pounds.
Since most of your extra weight is in your stomach and chest, losing weight through the sleeve could also make procedures like a tummy tuck or breast reduction possible in the future, as many surgeons require a lower BMI for those surgeries. If you’re considering the sleeve, you should consult with a bariatric surgeon to discuss whether it’s the right choice for you based on your health, goals, and lifestyle. It's important to understand that while the surgery is a powerful tool, long-term success still depends on making healthy changes to your eating habits and staying active. If you’re ready for that commitment, it could be a life-changing decision.

Yes you are a good candidate for this procedure. I would recommend you look into this and talk to a bariatric surgeon to discuss your particular case. I hope you find this useful. Congratulations. 
Dr. Alvarez