Is liposuction my solution to hypothyroidism weight gain?

Generally, any underlying metabolic problem should be completely corrected before considering liposuction.  I would urge you to work with your primary care physician and possibly a nutritionist.  If you and your doctors feel as though you have reached a normal baseline, then a discussion with a board-certified plastic surgeon would be appropriate.

This is difficult to answer without pictures and needs an in-person evaluation. For best results, it is recommended to be at your ideal or stable weight before getting a sculpting liposuction procedure. Liposuction is not a weight loss procedure, rather it is for sculpting and defining and removing problem areas that cannot be removed with weight loss and diet / exercise alone. With skin laxity, a tummy tuck or lifting procedure could be performed at the same time. I recommend getting a formal evaluation with a bariatric doctor or dietitian. Best, Dr. Emer

StarkA1997.   I appreciate your dilemma, however liposuction is not a weight-loss tool. Your best option is to fully control your hypothyroidism with medications, and then rely on diet and exercise to maintain your weight. Liposuction is a procedure designed to remove pockets of fat resistant to diet and exercise. Consult further with your medical doctor about treatment for hypothyroidism. Best of luck!

It is possible to lose weight, even with hypothyroidism.   You don't give your height and weight but your BMI will help dictate whether you should work on weight loss first.  Liposuction is always helpful but is not a weight loss procedure.   If you are continuing to gain weight, focus on that first.   See a board certified plastic surgeon as well and work toward both goals. 

No.  Liposuction will remove fat and contour the body, but it is not a weight loss tool. Very little weight is actually removed with liposuction and your best bet is to work with your endocrinologist to make sure that your thyroid hormone status is in balance. If there are areas after you lose weight that are residual and you're not as happy with your physique then that's the best time to undergo liposuction where you can get a nice sculpting of the body and achieve an excellent shape and contour of your body.

Hello!!
Thanks for the question and provided information as well. 
Without pictures it is hard to give you a recommendation. 
I recommend you to make an appointment with a board plastic surgeon for a good evaluation and to talk about your goals.
Good luck :)