This is correct. This is a reflexive verb that you are doing to yourself. This translates to, "Normally I brush the hair". If it was something like "Normalmente me cepillo el pelo de Anna" it would be incorrect because you are doing it to Anna, not yourself.
Tengo
tienes
tienes
tiene
Here is a little tip:
Yo(I) Tengo
Tu(You) Tienes
El/Ella(He/She) Tiene
Any verb for "Yo" ends in "o", "Tu" with "es"(with some exceptions), and "el/ella" with "e"(again, with some exceptions)
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hope it helps
Today I used a long dress in long sleeves with floral pattern and brown leather sandals