Welcome to Texas! Sorry about the situation you're in, but I think there is good news for you in moving to Texas, assuming that your garnishment is not from one of a few specific creditors. The Texas constitution will only allow garnishment of your wages by the IRS, a student loan, or from child support.
Hope that helps, good luck! If you need assistance of a good attorney, give us a call or another qualified attorney to see what your options are in protecting your wages.
I must respectfully disagree with my brethren just a bit. Your wages can be garnished under some circumstances. If your pay is made from a state where wages may be garnished, then the garnishment can continue.
You state that your company is in Texas, which leads to the idea that the garnishment should stop. That's usually true, but details matter. There are nation-wide companies where the pay is issued from a state that allows garnishment, and in such situations, you can't escape by moving to Texas. You'll probably be best served by visiting a local attorney with the paperwork.
I'm not your attorney; my answer includes assumptions. If you want me to be your attorney, I'm easy to find.