How can rid my body of bulging fat on my arms as I lose weight and exercise?

I have just begun a weight loss program.

I have hired a personal trainer and have been engaging in a weight training and cardio program with her.  One thing that I am very worried about is the large amount of fat the covers my arms.  I have areas of bulging fat that sags and hangs. If I measure it without squeezing the lose fat, it measures 19 inches around.

My trainer says that weight loss will help to make this area reduce. I'm curious if there's anything else I can do to prepare the skin for the weight loss.  I often think of liposuction but am really worried about that as I am diabetic.

Is there any advice you can offer with a situation like this? I have been concentrating heavily on a low-fat eating plan as well as my exercise program. But if there are supplements, procedures or products that can help, I would really love to know. There's all kinds of stuff (I assume scams)  on the net about this but I just don't know what I can trust.

Please help