Would my professional license still be valid?

Yes. Your professional license stays valid, because most licenses in Texas are already issued by Texas, not Washington. For the work you do day to day, your license is a Texas license now, and independence does not touch it. For credentials that cross borders, the world already has a well-worn system for recognizing qualifications between countries, and Texas would use it.

Most licenses are already Texas licenses

This is the part that settles the question for the large majority of licensed Texans. Your license to practice is almost certainly issued by a Texas board, under Texas law. Doctors are licensed by the Texas Medical Board. Nurses by the Texas Board of Nursing. Lawyers by the State Bar of Texas. Engineers by the Texas Board of Professional Engineers and Land Surveyors. Teachers, electricians, plumbers, cosmetologists, real estate agents, accountants: all licensed through Texas agencies. Washington does not issue these credentials and does not administer these professions. The authority that grants and renews your license is already in Austin, so independence does not invalidate it. It keeps doing exactly what it does now.

Your right to work in Texas does not depend on Washington

Because the licensing is Texan, your ability to earn a living in your profession inside Texas is not exposed to a change in sovereignty at all. The board that licensed you continues. Your renewal continues. Your continuing-education requirements continue. The patients, clients, students, and customers you serve are here. Nothing in independence stands between a licensed Texan and the work they are licensed to do in Texas.

Cross-border practice is a solved problem, used every day

The only place a question even arises is practicing in another country, and here the world built the answer decades ago. Professionals routinely have their qualifications recognized across national borders through mutual recognition agreements, arrangements that let someone qualified in one country practice in another without starting from scratch. This is ordinary, established international practice, not a novel risk. Independence would simply put Texas into the same system that professionals around the world already rely on.

The systems already exist, and the United States is already in them

Look at how routine this is. Engineers have the Washington Accord, an international agreement that recognizes the substantial equivalence of accredited engineering programs across countries, signed in 1989, with the United States as a founding member through its accreditation body. Accountants practice across borders under mutual recognition agreements, including one covering the United States, Canada, and Mexico. Nurses, architects, and other professions have their own recognition arrangements between countries. The point is that qualified professionals move between sovereign nations all the time, by design. An independent Texas, with world-class universities and a deep professional workforce, would be an obvious and welcome party to these agreements, and pursuing them would be a straightforward part of the transition.

Honest about what takes work, and what does not

Be clear about the line. For practicing in Texas, there is nothing to do and nothing to fear. Your Texas license is valid the morning after a vote and every morning after that. For professionals who need their credentials honored on the other side of a new border, negotiating recognition agreements is real diplomatic work, the ordinary kind every country does, and a serious transition plan includes it. The reassuring part is that the templates exist, the United States already participates in them, and Texas would not be inventing anything. It would be joining a system already in motion.

The bottom line

Your professional license stays valid, because it is already a Texas credential issued by a Texas board. For work inside Texas, independence changes nothing. For practice across the new border, the world's existing mutual-recognition system, which the United States already uses, is exactly the tool Texas would step into.