You know....at 5' 7", you're already at a healthy weight for your height and your body is likely to fight you getting any lower. Not that it's not possible, but most people find those last 10 pounds towards goal the slowest to come off and trying to actually get below a healthy weight for your body is going to take even more time and effort, even at induction levels.
Dr. Atkins recommends that if you have 20 pounds or less to lose that you actually start at 25 or 30 grams of carb per day (ongoing weight loss).
Has your doctor actually told you that you need to weigh less than your ideal weight? Most orthos that I know of would more likely recommend special exercises to strenghthen the back muscles and physical therapy rather than additional weight loss if a patient was already at a reasonable weight for their height because going lower than your ideal weight/body fat percentage carries health risks of its own. It's also no guarantee that you won't continue to have problems with your back.
How much you decide to lose is up to you, but be aware that it's likely going to be a difficult process even on low carb.