Rav Hai Gaon (according to the Sedei Chemed) describes Kabbalistic uses of specific chapters and verses from the Book of Psalms. You can recite the verses alone, multiple times or in conjunction with other prayers or actions. Shimush Tehillim is mentioned in Teshuvas HaRashba (413), by the Chida, and amongst other notable sages.
The Rambam in Hilchos Avodas Cochavim 11:12 pointedly writes: “Regarding one who incants over a wound or reads a verse from the Torah, and so one who reads verses to calm a frightened child or places a Sefer Torah or Tefilin on a child so that he will sleep – it is not bad enough that these people are numbered among the sorcerers and diviners, but they are also counted as heretics to the Torah by using words of the Torah to heal the body. The (words of the) Torah are for healing the soul only, as it is written, ‘and they shall be life for your soul’. It is permitted to recite verses and chapters from Tehillim for protection against troubles and harm - by merit of their recitation.