Although having hair of any kind might be a luxury for some, in general, luxuriant is the word you’re looking for to describe thick, healthy hair. Or anything else particularly prolific, lush, or abundant. Luxurious is best reserved for things that are expensive, elegant, opulent—think of a luxurious hotel or spa.
Both words come to us from the Latin luxuria, “excess, luxury, extravagance, profusion,” but, according to the Online Etymology Dictionary, luxurious seems to have spent some time indicating “lascivious” and “lustful” (in both its French and English forms), whereas luxuriant came more directly from the present participle of the Latin luxuriare, “to have to excess, grow profusely.”
Merriam-Webster Unabridged lists luxuriant and luxurious as sometimes synonyms indicating something “characterized by luxury,” but most usage guides, including Garner’s A Dictionary of Modern American Usage warn against confusing the distinct meanings.