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?

Yes, you qualify for gastric sleeve surgery based on your BMI and PCOS diagnosis. Most bariatric surgery guidelines recommend a BMI of 40 or higher, or 35+ with obesity-related conditions such as PCOS, insulin resistance, or other metabolic issues. Since your BMI is 39.5 and you have PCOS, you meet the criteria.

By BMI you do qualify for gastric sleeve. But there are other thing to take in consideration to. You shoul seek a consultation with a certified bariatric surgeon.
GR

Hello
Regarding PCOS and Gastric Sleeve :
In our experience the majority of our patients with PCOS have   a strong relationship  between insulin resistance and abdominal fat.   After having the gastric sleeve surgery these patients lose abdominal fat and insulin resistance improves dramatically.  80% of  our sleeve patients with PCOS experience a reduction in symptoms. 
Your surgeon will do a thorough evaluation  to determine if you qualify for the gastric sleeve surgery but results for patients with similar characteristics as the ones you list above have been very good. 

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