Luckily, the education and examination requirements in cosmetology for SC and Texas are very similar so it should be an easy process.
If you look at http://www.beautyschoolsdirectory.com/faq/license_sc.php, you will see that your current state are offering help with forms for moving to different states so it may well be worth contacting them.I looked at the Houston licensing website and they say that you should contact your current state (in your case SC obviously) just to tie up loose ends I guess, and to check that you have performed all the legal requirements.
However, the form you need to fill out to get your Texas license is http://www.tdlr.texas.gov/cosmet/forms/COS003%20Cosmetology%20License%20By%20Reciprocity%20Application.pdf
Just in case you want to check for yourself that your state requirements are similar enough to the Houston ones, the website I found the information on is http://www.tdlr.texas.gov/cosmet/cosmetstates.htm
You don't say that you tutor, so I assume that is not something you need to apply for, but just in case, the form for that is also on the above website.
Good luck with your move :-)