KoKo,
I used the Mifflin-St.Jeor method because you said you weren't sure how accurate the BF% calculation was
in case you (or anyone else) is curious, this is the formula for females:
10x weight (kg) + 6.25 x height (cm) -5 x age (years) -161
It is currently the most accurate way to calculate TDEE.
Anyway, what I got was:
BMR: 1065cals
TDEE: 1464cals
I have a feeling you are actually eating slightly less than you think (1000cals), especially if you are drinking the 600cal shake every day.
Basically, your body requires 1065cals just to function. In your day to day life your body needs 1464cals. If you get ~1500cals on a daily basis you are maintaining your current fitness level. As far as increasing calories, I would recommend the standard 10% increase: 1610cals or, since you are a small eater and this is kind of a big increase, you can start off at 5% caloric increase at 1537cals.
Keep in mind the quality of the calories is more important than the overall number - bingeing on donuts is not a good way to meet calorie goals
What might make more sense and be a little more tailored to you would be:
Training Day: 1640cals (12%)
Off Day: 1566cals (7%)
Since you don't weight lift more days out of the week I wrote up a quick little macro break-down for you as an example <3
Total Calories: 1566cals = 190g Carbs / 94g Protein / 37.6g Fat
*non-fibrous carbs*
I split up the totals into 5 balanced meals, but you can figure it out however works best for your lifestyle! Keep in mind you want to try and eat every 2.5-3hrs, this is optimum for your metabolism, keeps fat burning and energy up.
5 Meals of: 38g Carbs / 18.8g Protein / 7.52g Fat
Right now since you are trying to put on weight don't worry too much about eating carbs at night, etc. However, once you get close to your goal weight you want to cut carbs out from your last 1-2 meals and instead have a little more fat (so less fat in meals 1-4 for example).
Non-fibrous carbs are things like sweet potatoes, grains, etc. Please eat 2-3cups of veggies per day
the brain requires 150g of carbohydrates per day to function!
Protein bars like Quest Bars (my fav) can be helpful when you don't have the time or the ability to eat whole foods, but ultimately eating real food is better than supplementing with powders and bars
Best of luck with your weight training! Out of curiosity, what exercise did you do that caused strain on your back? I don't have any clients with scoliosis, though a majority of my clients have varying degree of 'back problems' ranging from slipped discs to general lower lombard strain. As you strengthen your body please don't neglect your core and lower back...they make up the "pillar" that helps support your whole body, and strengthening both parts will help overall upper and lower body strength!!