Hello my friend. Avoid that traditional dentist at all costs - once they drill that enamel, well, it is bad. In Britian, it is ilegal to drill teeth of people under 12 yrs old, and instead they use Ozone Ballons, which kills the decay [cavity], and it is cured, done, good.
To kill the bacteria causing the black spots, use a small amount of 3% Hydrogen Peroxide. Try using a q-tip soaked in the solution, apply directly to the black spots.This is another "oxygen" therapy, like Ozone used so extensively in Britian. It will not harm normal tissues, they like it.
Any health care professional will tell you that Hydrogen-Peroxid "is too hard on tissues". They don't want people using products that cannot be patented - try to find an example where they do, its not done. As a result, many of the best treatments are not used.
Non-patentable medicines are not profitable, and so despite their effectiveness they are ignored. I said it twice now...
If the black spots do not go away after a week of three times daily Hydrogen-Peroxid use, I will be amazed. Try to get the Food Grade, dilute it with distilled water to 3% or 3.5%, for best results. Hydrogen-Peroxid has many many uses around the home and in the body.
You should, of course, first try it yourself - whitens your teeth, cleans up the bacteria that should not be there, and if it stings just rinse. The taste isn't attractive, but not overly repulsive. Try some baking soda on a toothbrush after it sits for a minute or two.
It really is a beautiful thing, it is oxygen the stuff of life. And it has no patents, relieving the need to promote it with lies as most dental and medical products are.
Personally, I have used H2O2 to remove stains on my teeth. No problems.
ALLWAYS KEEP IN MIND THE DILUTION !!! Be carefull , it is potent stuff when full strength. But perfectly safe at 3% for "topical use" - but don't swallow it [little bits are ok to swallow] until you are fullly educated. See Ed McCabe's site for more info , but those links are being killed off regularly.