Update on my battle with reactive hypoglycemia: Skinny fat?

K2111ATIE

Height: 5'1".
Weight: Originally 175 pounds. Currently 128 pounds.
Body Frame: Medium-large.
Body Shape: Inverted Triangle/B-shaped stomach.
Pants Size: 8 (Non-plus size)
Shirt Size: XS - M (Non-plus size)
BMI: 24.2 (Normal)
Waist: 37 inches

Surprised at the last one? Me too. Unfortunately, I am very skinny fat on my bottom half. I'm happy with my body in clothes, but I look horrendous in a bikini.

Proof that I don't have a muffin top or anything. In this picture, I'm wearing size 8 skinny jeans, and a medium tank top from H&M.

http://i.imgur.com/8bwK4w7.jpg

Sadly, without clothes, I have a lot of fat deposits, especially on my stomach and upper arms. It doesn't protrude, as you can see in the picture, but when measured, it becomes very obvious.

My doctor wants me to start weight training right away because carrying as much fat as I do is very dangerous to your health. Unfortunately, I can't carb up because my blood sugar plummets whenever I do eat a high amount of carbs. I can get away with brown rice and sweet potatoes, but that's about it.

My doctor recommended that I eat protein before and after I work out, but I'm afraid that without carbs, I won't be able to build muscle very easily. I also only eat about 850-1,000 calories, since protein and fat fills me up. I can't imagine eating more.

I just got the book The New Rules of Lifting for Women, but I'm afraid it won't work.

Can anyone offer some insight? Thank you for reading this, and thanks for any advice that is given.