I'm underweight with prediabetes and high cholesterol

As the title says, I am very underweight (5'5, 98 pounds, female, 31 yo) with prediabetes and high cholesterol. This was diagnosed 2 months ago.

Everything online seemed to suggest cutting out carbohydrates and sugar, so that's what I did. I ate only lean meat and vegetables and drank water (with a lemon slice if I was feeling fancy).

Within one month, my weight was down to 85 pounds.

My sugar numbers improved BUT I felt sicker and weaker than ever, had no energy, my hair was falling out, and I was missing work. I couldn't do it any more and started eating pasta and rice again.

Do you have any advice to offer someone in my position? It seems like a lot of people are overweight with diabetes, or at the very least, a normal weight, and it wouldn't be detrimental for them to lose a few pounds but I rarely see posts from underweight people in my position.

I'm really at a loss here because I obviously want to improve my insulin resistance and cholesterol without damaging my health in other ways.

My doctor is completely clueless with this.

If you have any advice or tips I'd appreciate it a lot!

Edited to include my age