I am a 22 year old, 5' 6" and 244.5 lbs. My BMI is 39.5, I have PCOS. Do I qualify for gastric sleeve?

Hello
Thank you so much for your question and congratulation on taking the decision to become healthier. According with your BMI you can be a great candidate for bariatric surgery; but there are other factor to take into consideration before making a decision; in this case the procedure to keep in mind would be a revision. 
The sleeve gastrectomy, which reduces the size of the stomach is probably an excellent option because  the 70% to 80% of the stomach is removed and the part that produce Ghrelin which is a hormone that makes you feel hungry. Paired with healthy diet and exercise you should have a successful procedure. 
To qualify for weight loss surgery, the American Society for Metabolic and Bariatric Surgery recommends you meet one of the following:
1- BMI ≥ 40, or more than 100 pounds overweight.
2- 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.
3- Inability to achieve a healthy weight loss sustained for a period of time with prior weight loss efforts.
Have a consultation with a bariatric surgeon this will allow you to discuss about the different procedures in details. Many factors should be considered when deciding for a bariatric surgery, is needed to check your current health status with lab work and in a consultation you can accomplish this.  Don't be discouraged and continue searching the best option to improve your health.
Good luck in this journey