Is there a way to get rid of fatty deposits on my arms without surgery?

Fat on arms. CoolSculpting is a machine that draws fat into a suction cup and then cools the tissue. The cooling freezes the fat. The fat cells die. Improvement in contour is usually seen 8-12 weeks later. Liposuction can also be used. Best to see a board certified plastic surgeon to see your particular situation.
Yes, but. Liposuction can remove fatty deposits without large incisions, however in some people this will leave excess saggy skin :(.
NYC CoolSculpting. To avoid a surgical arm lift, which usually removes skin and lifts the sagging upper arm but can create an unsightly scar, liposuction has been done with good results in those patients who have good skin tone, but that is surgery. Coolsculpting uses cryolipolysis to freeze the fat without surgery and it takes one hour per site. We treat off-label as we await applicators for arms from zeltiq.
Likely not. . If i'm guessing correctly your describing lipomas. Non painful, freely mobile, rubbery masses. They can get quite large sometimes. Some folks may see them reduce in size if they lose weight, others may say they are more noticeable, but usually they don't go away without being surgically removed. You should be sure that's what they are by having your doctor take a look before taking my word for it.
Liposonix. As of dec 2011, i'm the first center in the U.S. To offer liposonix, the first fda approved noninvasive fat melting device. It's approved for abdomen and flanks but can be used off-label on other body parts. It uses high-intensity focused ultrasound (hifu) to cause lysis or destruction of the fat cells, nonsurgical liposuction. You can lose about 1 inch of fat (2.5 cm) per treatment per area.