Is liposuction during a breast reduction the best way to reduce bulk at the side and under the arms?

Either liposuction or dermolipectomy of the lateral breast can be the preferred choice depending on your shape and expectations. A photo may help in suggesting what may be more suitable for you, but the suggestion of surgeon who has examined you will be of more use to you. 

I have done this procedure many times with myself and a plastic surgeon. I do HI def body contouring and the surgeon will do the lift/implant at the same time. This will give you the best results. I suggest you see an expert who works with other surgeons at the same time to get your best results and can formally evaluate you to see if you are a candidate. Best, Dr. Emer

Becky.  Hard to answer without photos, but generally speaking, Lateral breast fullness best treated with direct excision and removal of redundant skin(your friend was right!). There are various techniques to accomplish this. Be sure to consult with a board certified plastic surgeon. Good Luck!