Wikipedia page on Dental caries. The thing to note here is that caries is caused by acids produced when bacteria eat carbohydrates. I think you've heard that sugar is bad for your teeth, but white sugar isn't the only type of sugar there is. Fructose and glucose are also included here.
A dentist will be needed to fix what's wrong right now, and you should take the pain and the cost if you are at all able to because you will have pain anyway, and if you're unlucky you might get a serious infection. However, reducing your carbs in the future should prevent (entirely or partly, depending on level of reduction) future holes.
Since you're saying that you don't want to use a toothpaste with flouride in it, you can do some research on
Sodium bicarbonate. I've never looked very closely at it myself, but I've heard a lot of people using toothpastes with this in it, rather than flouride, so it might be worth looking into!