Can I get liposuction? I'm 136 pounds and 5'6.

From the description it sounds like you are at ideal body weight. If several surgeons feel I cannot help you with liposuction it probably means they cannot.

My sympathies. The advice given on this page by many doctors should be very helpful to you. A thin person may have some localized pockets of fat, such as hip saddlebags that would look better after liposuction, but since liposuction is not a substitute for weight loss, patients who are truly overweight should lose weight first. Eating disorders such as anorexia are quite serious and patients can actually starve themselves thinking they are fat when they are not. So you should not be looking to a doctor, plastic surgeon or otherwise to help you lose weight or get liposuction.  Since you have already identified a problem, an unspecified eating disorder, you should spend your time and energy understanding that, and staying healthy. Once you get more perspective, then you can more objectively examine your body image.

Some patients certainly will go to multiple surgeons until
they get the answer that they are looking for.
With due respect, and of course without a photograph, if several board certified
plastic surgeons have suggested that you are not a good candidate for
liposuction, perhaps there may be some validity to this common consensus. I wish you the best of luck.