Yes, Texas is still a right to work state, although that has no bearing on your situation. Right to work means only that you cannot be forced to join a union in order to get work.
Texas is also still at at-will state, which is what I suspect you meant. It also has no bearing on your situation. It means that either party can end the employment relationship at any time and for any (legal) reason.
A non-compete agreement is legal. Whether the specific clause you refer to is enforceable, will depend on both state law and the EXACT terms of the ENTIRE agreement.
ONLY a local attorney who has read the entire agreement can advise you on the enforceability of the 150-mile clause.