It must be toothpaste, that is the feminine of toothpaste. In an etymological abuse, we can justify it as fixed on the inside, but the truth is that you there is.
The correct term is toothpaste, with tilde and the r after the f. Tooth care as such is a word that does not exist in our language. It means related to teeth or dentures. It is used for the hygiene of the teeth. Toothpaste.