Tourmanium is a stone made up of volcanic, elven and germanic rock, as well as tourmaline. Black tourmaline is used with the ALGIZ rune that is used for protection. It is also used in consecration and the banishing of negative energies. It is excellent for the operator to wear when performing dangerous rituals as it protects against negative energies
However the composition of tourmaline alone is a boron silicate mineral, borates are used in things such as fiberglass and bleach. The aluminum particles you mentioned are likely in fact aluminum as tourmaline is known to be compounded with this element as well as lithium which it may also be. Magnesium, sodium and potassium are also what comprises tourmaline.
We have natural elements of metals in our blood but the balance of it is crucial in so many aspects that don't just involve physical health. Fluoride has of course been shown to 'poison' the pineal gland which brings about issues with opening and activating our third eyes and sixth chakra. Borates have low toxicity in mammals but any toxicity that warrants a mention is something to be wary of. That toothpaste'll whiten your teeth alright but it sounds to me like it would be at a long-term and unhealthy cost, whether through accidental ingestion or entering the bloodstream through bleeding gums.
I would advise against it's usage in anything remotely close to consumption if I were you; this includes toothpaste.